Hi Christy,
The tomato flowers will pollinate themselves inside the bags so don't worry. Tomatoes cross at a low rate compared to some other veggies. I don't bag, and I have not had problems.
I don't have my Seed to Seed book handy, but I'm pretty sure eggplant will cross pollinate easily. The flowers are very open like pepper flowers, and peppers cross easily.
Beans and peas don't cross as easily, but it can happen.
The others I don't know off hand. I'll have to dig my book out tomorrow.
Remy

Hi Christy,
So sorry about my not coming back to the forum in awhile! Anyway, I got my book out and let's see...
Carrots cross very easily even with wild carrot aka Queen Anne's Lace!
Radishes cross pollinate with each other very easily.
Basils will cross pollinate, but if you can keep the varieties 150 feet apart(much less distance than most plants need for isolation!)you will be ok.
I double checked the eggplant. It seems the flowers are not very attractive to bees so that is why you've heard they won't cross pollinate. So they might, but chances are low like tomatoes.
Bees do like peppers so they will cross easily like I said.
I hope this helps you!
Remy