I spent a whole day trying to get a certain villager to move out testing how this works, and I found that the thought bubble victim seems to be chosen while loading up the game, eg. just after Isabelle's announcement. Once the thought bubble victim is chosen, the bubble stays on that villager all day.
If the chosen villager is inside their home or doing some activity, then you won't know they're the one with the thought bubble until they come outside. There's also a chance they have the bubble and just don't display it right away - though they usually do display it as soon as you start, but not always.
So your best bet is to start the day and quickly run around the town to see who has the bubble. If you find a villager who has it and it's not the villager you want to move - or you don't find any villager with the thought bubble at all because half of them are inside their homes or whatever - resetting the game immediately and then going back in - including listening to Isabelle's announcement all over again - will shift the bubble onto someone else immediately. The tricky part is you have to reset via the home screen before the game autosaves, which can be about 90 seconds after you've loaded up the day - I used the stopwatch on my phone. (If you're trying to do this you're best off starting at around midday when the crankies and uchis are out of bed)
If the game has saved after Isabelle's announcement, then the thought bubble will be locked onto the chosen villager for the whole day regardless of whether you saw it, when you saw it, and whether you responded to it or not. Resetting won't shift it after autosave. The next day it will shift, but whenever it shifts there is of course a one-in-nine chance it will shift back to the same villager.
This is based on my own experiments and I am not an expert by any stretch. So if anyone has any contradictory information, by all means consider that too!
You don't need to avoid talking to Anabelle even if she has the bubble. Just make sure you only talk to her when she isn't showing the bubble, and if you accidentally do talk to her and she asks to move, hit reset via the home screen. It's fine to talk to her while she's just walking around normally without any thought bubble, even if she did display one earlier in the day.