d20 Modern rules and whether they'll be incorporated in 3.5e aside, here's where things stand by my interpretation:
Shield bash attacks can be made by using the shield as an off-hand weapon.
Shield expert lets you retain a shield's AC bonus when the shield is used in an off-hand attack.
Ambidexterity ignores all penalties for using an off hand. From the reading of Ambidexterity, that means handedness and primary/secondary attacks have no relation in and of themselves as Hypersmurf earlier suggested. Granted, it would take extraordinary circumstances for anyone to willingly make a primary attack with their off hand outside of shield bashing. For example, your primary hand might be broken or stuck in a trap so you have to use your off hand. I think the S&F authors gave a nod to The Princess Bride by making Ambidexterity a requirement for duelist. "I'm not really left-handed."
Without Ambidexterity, making a shield bash as your primary attack will suffer a -4 penalty and you can only add 1/2 your Strength modifier to damage. With Ambidexterity, the attack suffers no penalty and can enjoy the benefit of your full Strength modifier to damage.
I wonder if all those people boasting about the Divine Shield smackdown that Paladins can do take this into account. Because without investing in a 15 Dex and taking Ambidexterity, their shield bashes would be made with a -4 to the attack roll and with 1/2 Str mod to damage. With 25 pt-buy stats that 15 Dex is a huge investment for any character, but even moreso for a Paladin. And even with higher pt-buy or rolled stats, that's a precious feat slot.
A Fighter wanting to focus in shield bashing has it a lot better off. Dump into Strength, take 15 Dex and Ambidexterity, and have loads of fun with Shield Expert, Power Attack, Improved Shield Bash, and Shield Charge.

If you're a human, you are rocking and rolling as early as third level. Other races are rounded out for shield pimp action as early as fourth level. For min/max fun take Weapon Focus and then Monkey Grip with a polearm so that you can also threaten at 10 ft.
One thing I am a bit confused about are the mechanics of Improved Shield Bash. From how I read it, the utility of this feat is that you might be able to knock a creature 5 feet away so that when you take a 5 foot step away from the enemy they are then only allowed to attack by moving forward or charging, unless they have reach of course. The text of the feat says that "any shield bash" you take acts as a bull rush, but would it be logical to state that the player can opt
not to exercise that option? Because what if you have multiple attacks and knock them back with the first? If I had a character with this feat then I'd save that for my second attack unless it had no good chance to hit. If using the Monkey Grip a polearm tactic vs. an opponent without reach this could get pretty cool. Shield bash, 5 ft. step away, and take your AoO with the polearm if/when they close to attack on their turn. Wash, rinse, repeat until dead.
My Shield Basher, Human 25 pt-buy
Str 15, Dex 15, Con 14, Int 9, Wis 10, Cha 8
Fighter 1: Ambidexterity, Power Attack, Improved Shield Bash
Fighter 2: Shield Charge
Fighter 3: Shield Expert
Fighter 4: Combat Reflexes, +1 Str
Fighter 5:
Fighter 6: Weapon Focus (polearm of choice), Monkey Grip (polearm of choice)
The 4th level feat is open to anything. Weapon Focus (shield) and then Weapon Spec. (shield) later, turning the +2 damage into +4 when charging. Power Lunge could be a nice complement to Shield Charge if you don't mind the AoO. Hold the Line is also an option. Never underestimate the value of Close-Quarters Fighting vs. monsters with Improved Grab. If you dock your Con and take 13 Int you open yourself up for Expertise -> Improved Trip -> Knock-Down, which means those heavy shield hits might knock them 5 feet back and flat on their arse, too.

But I figured those feats could wait and chose Combat Reflexes to take full advantage of the polearm's 10 ft. threat range coming up at level 6.
You're not going to be able to make a primary shield basher as effective as a more regular fighting type, pretty much no matter what you do.
Behold the power of cheese, Dan.