When you say "dirt tires", do you mean the stock dual-purpose Bridgestones the bike came with, or some other brand of more dirt-oriented tire?
After I bought a 2009 WR-250F for my off-road riding, I spent last season riding my 2008 WR-250R as my street sport bike.
I used the stock Bridgestone tires the bike came with, and when they wore out, I bought some more of the same tires.
I feel they worked very well, and being that, as I mentioned, I rode it like a 250cc sport bike, grip on the road wasn't lacking.
Anywhere from 0-80mph (my bike's top speed), they felt rock-solid.
I used 18 psi in each tire.