So how do either of you rule it and how un-RAW does it get. Do you allow a pc to stow a bow, draw a weapon, and attack?
No, because stowing a bow is more difficult to do, for one. It takes your focus away from the action immediately in front of you, and it's even more difficult if you're wearing other equipment, armor, a cloak, or whatever, and it's going to require two hands to do.
Also, in regards to dropping the bow, although I noted that I allow it because dropping it is relatively easy to do, like anything, it's also a question of circumstances. Historically, charges were often effective in battle because they gave the enemy too little time to react. If they wanted to shoot their bow (or arquebus or musket later on) against those charging, it generally gave them too little time to drop their bow and draw another weapon to defend themselves. In essence, they would have advantage on the side that's charging at them (if their nerve held up), but then the charging side would have advantage against them because they weren't prepared to defend themselves. A single shot from an arrow or early firearm could drop (not necessarily kill) their target, and the hope was that enough of them would drop to disrupt the charge. Otherwise you were relying on somebody in the second or third rank to be prepared to defend against the charging opponent.
So really my answer is that it's much more circumstantial. I prefer the rules to not have fixed results, and allow the circumstances to alter the chances of success. So attempting to stow a bow while actively engaged in melee would probably result in your opponent having advantage on his next attack (if his turn hasn't occurred yet), or granting an opportunity attack if it has.
We base our adjudication of the rules (or change them if necessary) to allow us to recreate whatever combat scene we'd like. So we look at the actions and circumstances and apply advantage, disadvantage, and opportunity attacks depending on those, rather than a rule that says "if two minis are in this position on a battle mat, you get this." This applies whether we're using minis or not.
So for something like flanking, if you're in the open, you almost always need to have three people to flank somebody, since generally as long as the target keeps moving it's tough, though not impossible, to flank them with only two people (to the degree that one or both of you would get a 25% increase in their chance of success of your attack). On the other hand, if you're in a hallway, and you can get one person on either side of them, then it's much easier. Of course, the target's best option at that point is to try to get past one or the other of you.
A lot of it depends on what you're looking for out of the game/combat rules. Some folks like the idea that certain moves or maneuvers always work the same way, produce the same results, and focus on trying to set up the situation so that they can always use their "best" option every round. To us, combat doesn't work that way. Gaining an advantage is quite difficult. Imposing disadvantage is easier. In our campaign, imposing disadvantage puts the target on the defensive, attempting to end whatever condition or position that's impacting their ability to fight. Advantage, on the other hand, can often end a fight. A target that's knocked prone and disarmed for example would know that their chance of survival just dropped considerably, and then it's really a question of how good they are (or think they are), and whether risking death is worth not surrendering/being captured.