Two things will get you a "faster" bike. Tires more suited for the road (skinnier and low profile street tread) and a lighter weight frame.

If you want to look at new bikes, go to www.konaworld.com and look at their Asphalt line of bikes.
They have some great value bikes and some are an easy transition from mountain bikes.

Do you do a lot of gear changing now? I'm in houston and I don't so I've been doing the single speed thing lately. You still get a freewheel as opposed to a fixed gear. Also about to try an internal geared hub on my Riv.

Straight bars, drops, or other is personal preference.