It depends on how you do it.

I would decide who you most would like to play with and contact her first, with enough advance notice so she has time to get back to you. How long that is may be stated on her site (e.g. 24 hours, 3 days, 1 week).

If you have not heard back in that time, contact your second choice. And so on.

Make sure you let the Domme know the specific time you're available to play. "Mistress/Goddess/Ms./etc, I will be in town next weekend and only have availability on Saturday at 2pm for 2 hours. Would be able to see me then?"

If you are in a position when you aren't going to know until the last minute, then just be prepared for an outcome that matches that.

If I receive a request from someone, whether they indicate they're in town briefly or not, and they end up not replying back to me, I usually don't think much of it. I know some Dommes are bothered by this and take it personally. I don't unless the person contacts me more than once and doesn't follow through.

If you do end up getting multiple replies and can't see everyone, just send a brief message to the Domme(s) with whom you're not booking. Thank them for their time and say you will be unable to session after all. Depending on how many messages you may have exchanged, a small tribute or gift is always a way to show respect for Her time.