I usually run then go out for a bike ride. By the time im done running, my tshirt is drenched. Is it okay to ride with with alot of moisture? SHould i change to a dry shirt before starting my ride?

I'd advocate changing it immediately. If you cool down in sweaty clothes, you leave yourself susceptible to colds. I know this from very recent experience.

If you're not already, try using a shirt made from a moisture wicking material. This will keep most of the wet stuff off your body.

Coolmax is great stuff. You could also run without the shirt.

Dan