As another guy in ballroom, stick with it! Good things will come.
First, don't depend on the dance-partner websites, especially the ones that charge a fee.
This is true. Just as most women on Match are looking for a rich attractive guy, women on the paying sites are looking for a partner, er, free teacher. They are dirtbags. Good for pros, bad for amateurs.
I need to make it clear that I mean a DANCE partner and not an object of romance.
Pretty much this for the early stages. However, as a guy, if you advance and want to travel & compete, girlfriend & dance partner better be one in the same. I've lost a few potential girlfriends while in the mid-stages due to cro-magnon minds.
It is very important that you do NOT let yourself "become enamored" of your instructor, a nearly universal pitfall for beginners.
This is serious, and is a very dirty aspect of how studios try to keep guys. If you sense that your instructor is playing the filthy strip club girl card instead of that of a teacher, get out of there. Too many of them try that in my area. Go find an instructor who has more of a "best friend" personality for beginner levels - it's much more rewarding. Oh yeah, and you have a new best friend to add to the bunch.