A.M.
I would agree with the other posters that this is experience is not the norm. The volunteers usually only have about 3-5 kids to watch in their group, unless they don't have enough parent volunteers. And the parent volunteers all get to ride on the bus with the kids.
Not letting her go is extreme, and realistically are you going to do this every year for the rest of her school years? She's going to have MANY more field trips in the future. The kids are safe. They usually have them all wear a similar shirt or same color or something so they are all spotted easily (if not, dress your daughter in a bright shirt that day).
And another way to prevent what happened before from happening again -- tell your daughter to go to the restroom AT SCHOOL before they get on the bus. The teachers usually offer this up first and try to demand it so no kids will have to go to the restroom once they are at the destination.
I would do whatever it took to be a parent volunteer on the field trip, especially hearing the concerns you have about field trips. they usually need as much help as possible. I would take a taxi there if I had to. but I'm sure someone - a friend or relative - could give you a ride to the school. Once there, you just ride the school bus with the kids.
the only way you'll be able to calm your nerves about this is if you personally go to watch your child (and you'll be in charge of other kids, too). I know there's nothing anyone can say that will ease your mind about it, so I would do everything possible to just go and be a volunteer parent on the trip. It sounds like this is a really big issue for you.
UPDATE: check with your teacher, but I know in my school district all volunteer parents that pass the background check (which you need to do in advance of going on the trip or any volunteer opportunity) can and should ride the school bus with the kids .... the parents are supposed to help keep order on the bus as well - remind the kids to sit backs to back, not stand, etc. So as long as you go through that background check -- you should be able to ride the bus with the kids. But I know you will probably not be able to take the younger ones with you -- this is a trip for the class. So you would need to find a sitter for the younger siblings.