Assalamu alaikum wa rahmatullah,

What advice would you give to a single Western woman who wants to study Islam at the level of scholarship and not only literacy?

There are no Islamic higher Education organizations near enough to me, meaning that to gain scholarly knowledge, I would have to travel.

Walaikum alsalaam wa rahmatullah,

Firstly I would like to thank you for your concern and interest in learning the deen at a higher level, and that is one of the greatest acts of worship that you can do.  To obtain a scholarly level of knowledge of the sharia you need to work on mastering the Arabic language or at the very least having a strong understanding of it, studying the Quran and it would be recommended to memorize it the very least memorizing the ayaat of al-ahkaam (Verses of legal deduction), studying fiqh (jurisprudence) through one of the well recognized madhabs (schools of thought) and before all of that, having a strong understanding of the Aqeedah of the early generations, and I would highly recommend the books of Shaykh Al-Islam Ibn Taymiyyah in this regard.  Most of this should be done under the supervision and instruction of a scholar.  

I understand that there may be no direct access to most of these resources in your locality but with modern technology there are so many scholars that you can benefit from via recorded lectures and online classes.  I am sure that if you look locally you might find people who can help you in certain areas like mastering your Quran recitation or basic Arabic lessons.  After that you may need to travel to a Muslim country to pursue an academic career in one of the known universities.  

May Allah give you tawfeeq and success.