Will Bantam roosters try to mate with Rhode Island Red chickens?

YES. We didn't think it could happen so we let one little Bantam hen keep an egg because she wanted to lay on it. Then all of a sudden I am checking for more eggs and BOOM! We had a baby chick. We were shocked. We have two Rhode Island Reds and an Egyptian-looking chicken. We are pretty sure he got to the Egyptian-looking one because we always see him trying to get to the Rhode Island Reds, but with little success. Now our little Bantam rooster is actually a very large Bantam... his dad was less than half his size and he some how turned out huge so maybe this influenced his ability to get up there! Another view:

They will certainly try, but most Bantam roosters are too small to 'make it'.

If a bantam rooster is the only male in the flock the hens will often make adjustments for his size. The hens will flatten out or squat down fluffing their feathers after he does the signal dance. (the rooster dances side ways around the hen he has chosen to mate with) The rooster stands on the hens back and mating takes place.