Yes. At the first hint of frost, they'll turn their toes up; in London, we don't usually get a frost till very late October or first week of November, where you are, it will iikely be earlier. The bulbs need to go in, you're away for a month anyway and won't even see the begonias if you leave them in situ. You haven't said which bulbs you're planting - many are fine being left till November, but others aren't. Just do it - if you can't bring yourself to bin the plants and they're just the little bedding begonias, transfer them into the garden somewhere if you've kept the roots more or less intact and water in well. If they're begonias with corms/rhizomes, then put them somewhere to dry out and store them for next year.

I agree, you are not going to be there so it wont matter. you can lift the begonias if they are the tuberous ones and repot them until they die back.

Thanks Bamboo they are tuber begonias. I did take your advise and lift them. Just plucking courage up to lift my dahlias as they are gorgeous but I need the bed they are in for tulips and daffs.