You can learn to do a back-handspring in that time in your tumbling class if you work hard and particularly if you can put some time in on conditioning outside of the class.
However that won't enable you to teach it to other people. Even a qualified coach would have difficult teaching it to a group of gymnasts who were at a stage where they were ready to learn it in only one class and the people who would be in your class would not be at that stage. The idea of trying to teach bhs in one lesson to people who probably can't do a handstand, bridge or backwards roll hollow out is crazy and pretty dangerous.
Also would you have the resources (mats and so on) and would participants be appropriately attired? If so you may be able to use some more basic gymnastics move such as forwards or backwards roll or possible handstand or cartwheel. There is some possibilty for differentiation here as well. For a handstand: handstand free, spotted, against wall, front support with feet raised on box or held by other participant. For cartwheel, bunny hop over box, bunny hop over, "baby cartwheel", bent leg cartwheel, straight leg cartwheel. For forwards and back wards rolls these can be performed with a spot or down a foam wedge. This would be important since participants are likely not going to achieve the ultimate goal (unless they were there already) so you would need some other method of showing progress towards that goal in order for the class to be successful.
However given that your class will consist of a physically disparate group and that the ability to do any gymnastics move is not determined only by knowledge of the technique used in the move but also by physical ability I think you would probably be better of picking something else. You want something where you only need to know the rules of how to do it in order to get some sort of successful outcome, without a lot of prerequisites and other factors.
If you are going to do something physical teaching them some dance steps or a simple routine would be more appropriate, less risky and wouldn't require equipment.
Practice
Work on back flexibility. Also practice back walk overs. If you already have a back walkover then try doing it with your feet together (this is just a slow back handspring without jumping). Also practice on a trampoline or into a foam pit to make you comfortable doing it.
You can get it in 2-3 days honey.... Just practice :)