For the immediate situation, if Bill hasn't picked a time after 10, just send another email saying
sorry, I spoke too soon, 2-3 is not available after all.
Now since this might make Bill feel bad, and also make you feel bad, you might want to adopt the habit of reading all the emails (or at least their subject lines) before replying to any of them. I whip through deleting spam, and just noting who various emails are from, then read the ones that seem like they might be immediately and personally relevant. After reading all of those I can reply to them all or files them, and then I can skim through the various mailing-list messages that were less urgent.
If Bill had already asked for 2-3 by the time you read the "reschedule" email from another person, you would just have to reply and say
I'm not available then - how about any time between 10 and 2?
Since that's a little awkward too, it also argues for reading everything before starting to reply.