I am a teacher too! Yes, if you are going to be out of the house for an extended period of time it is a great idea to keep a complete travel kit with you. My ET nurse gave me a little Hollister bag that came with scissors and some little garbage bags. We added paste, a wafer, a pouch and skin prep to it and I always bring it with me if i'm going out for a while.
If you've only been out of the house a few times I would suggest going out more often just to get used to being out with a bag. That way when you do start working you will feel more comfortable and probably less self-conscious about having an ileostomy. When I went back to work at learning centre that I have taught at off and on over the past 3 years (only my bosses know about my surgery) and was able to be there without anyone knowing or suspecting that I have an ostomy my confidence really began to build. It helped me realize that I can adapt to having this ostomy for a little while. Mine is not permanent but I will have it until at least December. Good luck to you!