How to get a girlfriend who's serious and potentially long-term?

I'm generally somewhat outgoing, but nervous when it comes to physically putting myself in close proximity of unfamiliar women. I'm in my mid 30's and want something that can start casual, but possibly turn into something long-term. My teens and early 20's had a few short relationships, but usually due to living in an apartment with a lot of tenants who weren't long-term and so variety was plentiful. Dating sites simply don't work for me. I just need help!!!! Thanks.