All you need to do is focus on building up your towns and economies, once you have a tonne of money, just keep checking all the towns. Easiest way to do this is build a warehouse in every town so you don't actually have to travel there. Once done, find a town that has a teacher then save it before talking to him. Once done, just stay on the city info screen and fast forward the time to see how many days pass in between his leaving and someone else turning up in the tavern (anyone at all, not just a teacher). That is your window of waiting. Once you have the number of days in your head, reload and search for all the teachers in every city, speak to them and utilize them if you can, then fast forward that number of days, then check and again. Rinse and repeat.
To be honest though, this shouldn't be a problem, I got it buy buying the last 6 or 8 upgrades I needed whilst I was going around taking over towns peacefully. It all went by pretty fast.