Hi DDE- I recommend asking your lady to stock your favorite after you've visited at least once. Bringing your own on a first visit & suggesting using it may put a lady on edge, to answer your question.
A suggestion instead of purchasing multiple varieties to try- if you have a session and notice you liked the fit and enjoyment more than another experience, just ask her to show you the package so you know the "make & model" that you prefer.
Of course if you have a regular lady you see that you are well-established with she will probably be ok with you supplying your own. Some ladies will expect you to present them still sealed in the manufacturers box, which is fair IMO.
As with most purchases we make as consumers, check reviews
A great condom source is www.undercovercondoms.com where you will find a vast variety of condom reviews by men and women. Only you know your likes, dislikes, size, etc. Reading the reviews will steer you in the right direction.
In regards to you asking permission to bring your own, I hate to state the obvious but please don't do that if you've never met her. Even though you mean no harm and are only attempting to make your experience more enjoyable, (speaking for myself) being asked that would scare me away no question.
Good luck on your favorite condom quest!
Peace,
Astrid