Finding a good mentor can be difficult as good mentors often have a full list of good prentices.
To have a good mentor you need to be a good prentice. For most of us that means composing your pets
ALOT. It also helps if you get a decent amount of experiance.
Your mentor needs to be online at the same time of day as you are since you dont get BP share when they are offline.
Your mentor should be high lvl, over 500 BP hopefully and be a lvl 8 or higher mentor, of course 10 is best
Keep in mind that after you are lvl 125 it will hard to impossible to get a good mentor, so find one early.
If you leave your mentor you lose some exp and you can not get a new one for 3 days.
If your mentor kicks you, you will not lose exp and you can get a new mentor immediately. So keep that in mind if you intend to change mentors.
Also make sure you have a new mentor agreeing to take you before you leave you old one. (Unless of course it is someone who quit the game.)