Tri Bars vs Normal Bars

And so are "tri bars" in the sense of bullhorn style bars.  In USCF road and crit events you are only allowed to run standard drop style bars.

If you are doing organized/sponsored charity rides or riding events, then just read the rules for the event to see what they allow.  (And not to be too much of an arrogant roadie snob, but those types of events are NOT races - pet peeve of mine when people call them that).

Well, you're talking about two different types of bikes here, and not the same type of bike with different bars. The bikes that come with "tri bars" (pursuits with aerobars) are tri bikes, and they have a totally different frame geometry than a bike that comes with "normal cycle bars" (drops and horns), which would be a road bike. It is not suggested to put pursuits on a road bike, but you can certainly add aerobars to the road bike bars.

If you plan on doing road racing and tris, and only want one bike, then you should get a road bike. You can add aerobars to them when you'll need them (for a tri), but remove them when you're not allowed to use them (for your road races). You just won't be able to shift from the end of the aerobars with that setup, but it allows you to use the same bike for all your different races, with the best possible set up. Now, if you get fitted, a "tri" fit on a road bike and a regular road bike fit on the same bike will be a little different, so you might end making a few other adjustments to your bike when you add or remove the aerobars.