#1 If you haven't not gained it yet, how can you be denied the ability to use it? In practice though, you just shove the creature and worry about the action economy later. You don’t know if you can use a bonus action yet, so you’ll just have to wait and see.
#2The condition is that you take the Attack action on your turn, so later, on your turn, when you do, you’ll be able to use a bonus action, which you can choose to take at any time during your turn because its timing isn’t specified by the feat. Therefore, you can apply it to the shove attempt you made.
#3I understand how your interpretation works. But even this sentence you've written can be interpreted to mean you can buy the book first as long as you end up getting the money later. Maybe there's a certain amount of cash that needs to be kept on hand for some other purpose, so the cost of the book will need to be replaced.
#4I'm not suggesting you use a bonus action to shove a creature without also taking the Attack action on your turn.
#5I'm not sure what you mean by "time-travel". I'm certainly not advocating for either players or characters to travel through time. If all you did on your turn was to shove a creature, then you took the Attack action when you did so. In the case of Shield Master, "taking the Attack action" doesn't correspond to anything in the fiction different from "taking a bonus action" as long as at least one of your attacks is a shove.
#6Personally, I don't like it, but I'd still play with a DM who made such a ruling even though I think it's a bit misguided. It's a valid interpretation of the rules-text
#7I think you're saying if you have Extra Attack, you can shove a creature with your first attack then get two more attacks (possibly with advantage) using TWF. Without Extra Attack, I don't think shoving a creature counts as making an attack with a light weapon, but I suppose that's up for debate.
#8It isn't just Shield Master. It's the way many bonus actions were designed. I actually think it was quite ingenious that they attached the Shield Master shove to the Attack action because a shove is a melee attack, so it's potentially very flexible, given the right interpretation. Where they ran into trouble, however, is with the eldritch knight's War Magic feature because a weapon attack isn't part of the Cast a Spell action, which is from where Jeremy Crawford's revised ruling comes.
Sorry for the late reply today (busy) and I know others have brought up some points, but I don't have time to digest it all before I hit the sack. So, please forgive any redundancies. I've also added the numbering to address your points.
#1. You are denied the ability to use it because you have not satisfied the requirements to gain the Bonus action feature. If you argue you can take the Shove first and not worry because you'll have to wait and see, think about what you are doing. What if you use your Bonus action to shove, and then are denied your Action afterwards and cannot take the Attack action? Does the Shove have to be unresolved now because you certainly didn't take the Attack action on your turn! Here is a perfect scenario where this could happen.
You are badly injured and have only 5 hit points remaining. You are fighting two foes and decide to use your Bonus Action to shove one and your Attack action on him with advantage. However, you use your Bonus action and succeed, the opponent is knocked prone! Wait! Unknown to you, the other foe has the Sentinel Feat! Since you Shoved, which is a special attack but an attack nonetheless, he uses his reaction to make a melee weapon attack against you! He hits! A crit! You take 10 damage and fall unconscious. However, the universe is askew, how can this be? Don't you have to take the Attack action on your turn since you used the Bonus action granted by Shield Master to Shove earlier?
This is why your reasoning falls apart IMO. You cannot benefit from a conditional feature before you satisfy the condition to gain it. In the scenario you Shoved before you took the Attack action and were unable to take the Attack action, therefore you never should have been able to Shove.
#2. This of course ties into the next point. As you say, "...so later, on your turn, when you do [take the Attack action], you'll be able to use a bonus action, ..." Notice what you wrote: "you'll be able" as in "you will be able",
will, as in future tense, which follows you writing "so later, on your turn". You have just written that later you will be able to use a bonus action. Later, as in after the Attack action has been made.
#3. You have no other cash, this is why you must go to the ATM to get cash in order to buy the book.
#4. But you are, inadvertently, when you use a bonus action to Shove before taking the Attack action. The scenario I pointed out in response to #1 shows how this could happen.
#5. I meant time-travel because of the paradox potentially created and demonstrated in the scenario for #1. I do notice, however, you seem to think:
"If all you did on your turn was to shove a creature, then you took the Attack action when you did so. In the case of Shield Master, "taking the Attack action" doesn't correspond to anything in the fiction different from "taking a bonus action" as long as at least one of your attacks is a shove." Shoving a creature, in and of itself, does not constitute taking the Attack action. Your statement seems to reflect (correct me if I am mistaken) that by using the Bonus action to Shove, you in fact took the Attack action when you did so? If that is your reasoning, IMO your logic is flawed because taking a bonus action is not the same thing as taking the Attack action, even if both actions are used to resolve a Shove. The first is a bonus action where you are permitted to try to shove a creature, while an Attack action can be used to shove or make other forms of attacks.
#6. Well, I am glad we seem to agree that even in our disagreements we could still play a game together.

As I have stated in other posts, I prefer the idea that the Shield Master feat would confer a Bonus action without the Attack action having to precede it, but unfortunately for us that is not the official ruling as I understand it. I hope my DM will house-rule it the other way, but I'll continue to play in his game as well, even if he doesn't. Since you agree it is a valid interpretation, I won't try to persuade you otherwise except to finish this post unless you wish to continue?
#7. You are correct in both points here. I am saying, if you have Extra Attack and TWF, you could use the Attack action and your first attack to Shove, knocking your opponent prone. At which point you still have your second attack via Extra Attack
AND your bonus action granting you another attack via TWF. Both of these attack would be made with advantage. Without Extra Attack, shoving a creature
WOULD NOT constitute making an attack with a Light melee weapon, so you would not gain the bonus action attack from TWF. To me there is no debate on this because shoving a creature is not a melee weapon attack at all and I would have to dig, but I remember reading that either in one of the core books or maybe SA.
#8. This seems to return to #5 in that your wording indicates you understand that the bonus action Shove from Shield Master counts as its own satisfying condition because it is a melee attack. In the X,Y logic, that would be like arguing this: "If X, then Y" becomes "Since Y, then Y." You are trying to equate Y to X, but they are not the same (again, see #5 above).
Maybe that clears things up or not? If you are stuck in your own understanding, I don't know if anything more I have to say can convince you otherwise. I think the scenario in #1 shows it best how you must first take the Attack action before you can Shove (at least as the official ruling is concerned). I agree I like it better the other way since it adds an offensive element to Shield Master without having to rely on allies to benefit instead of you. But, I am not JC and I don't make the rules, I can only encourage my DM to house-rule otherwise.
