how many single moms............  

I waited six almost 7 years until I started dating and it was well worth it. I too, did not want to share, I so know what you mean. It is hard enough to find time for yourself being a single mom, let alone time away from your child WITH a new person as well. And will that take up all your precious alone time, make too much time away from your child, fight feelings of being selfish, not only of your time, but of belongings.?.?? I felt I had a firm knowledge of what I wanted out of life and out of this extra person that I could bring into my life (as well as what I did not want, which is very important!).
We started VERY slow. He knew about my son from the beginning. Maybe I was just lucky or maybe it was just happened to be. because it wasn't like I said to myself, "OK, I'm ready to date. I'm gonna go get myself a man!" I was starting to get lonely and I wanted to meet someone but like I said I really didn't put my self out there. I started to hang out with friends a little bit more, you know, share my time with them. I started to meet new friends, friends of friends, and further developed those relationships. Then I took the leap, I actually told this guy, my current boyfriend, that I was interested in him and wanted to get to know him a little bit better. BUT, I made clear from the beginning, that I was not looking for a replacement father for my son. Although, if he was going to be a semi-permanent fixture in my life he had to figure out how he felt about having a child in his life as well, because if he couldn't handle it I wasn't going to waste my time. Don't get me wrong, he's a very nice person but that would be a deal breaker and it had to be known from the beginning.
Since we went very slow on the whole spending lots of time together and relationship "things" though, ie: sharing space... things have worked out great, but like I said I was ready we went slow and slowly introduced him to my son as an on-going fixture in our life. It did take some adjustment, on all of us, but we made it and we are a functional happy "family" now!
Lots of luck to you!