I wouldn't use a bailout bottle while teaching, unless you're teaching solo diving. You're sending students the message that diving the way they are, with a single tank at recreational depths with a buddy but no bailout bottle, is not safe. I know you don't intend to send them that message, but what if one of them asked "why are you carrying the pony, and if it's necessary, why aren't we carrying them too?" I mean, if it's OW classes, you're teaching them specifically to share air, do CESAs, watch their gas carefully, and otherwise dive safely....yet you're demonstrating that you're not comfortable doing the same.
Bit of a snarky point, I realize.....sorry about that. It is something to think about though. I have a 13 cft pony that I've used diving exactly once in several years. But it's convenient for working on regs and filling tires.