Oh about how wet my fabric is.. I have tried dying shirts while their wet and while their dry and while it seems that the dryer ones are easier to control colorwise, sometimes the dye just wants to bead off without even soaking in. I did have pretty good success with a shirt that was only slightly damp though. Im using 100% cotton shirts.
Yeah--the beading is something to overcome! Consider giving the surface of the tied bundle a quick spritz with water or water with a few drops of synthrapol. That primes the pump on the surface to get the absorption started. I also squeeze the bundle to help force it in and reapply the dye repeatedly--stopping when dye pools (unless that is what I want--can be a cool effect), then adding more once it is absorbed.
Bleeds can be a real bear, but I have come to enjoy wringing and forcing the dye into place. Missing a little bit can be very cook too as you can get these brilliant white areas in stark contrast to some deeply saturated areas. It really works in some circumstances. Where it does, I'm less careful and let random chance come into play. Where it doesn't work, I am extremely careful.
Get things up around 100 degrees during the cure and you ought to be able to pop things out easily in 6 hours or even less.
Gee--now I feel like dyeing--it's been ages.
Have fun!