Depending on your specific matching criteria, you could be matched in as little as a few days or a week, or it could take you much longer. Being single is not an issue at all. A great many surrogates that I know (both online and IRL) have carried for single IP's....men and women. And sexual orientation hasn't made much of a difference either. Surrogates tend to know who they are comfortable carrying for and their profiles aren't shown to IP's that don't meet that particular requirement. The bigger points are number of embryos to transfer, if the IP is intentionally wanting to try for multiples, how both parties feel about termination or selective reduction. If there is a geographical requirement, etc. While surrogacy is generally a "hurry up and wait" game, it can and has moved very quickly for some, once the process is started. You can figure that it'll take about a year to match and move forward, then find you match in a matter of a couple of weeks and then what? If you're not prepared to move forward at that time, you have to hope that the surrogate is willing to be on hold for however long, and depending on the connection, there are surrogates that aren't willing to wait an extended period of time before cycling. Other's are just fine waiting until you're more prepared.
My 1st IP's were told to expect 6mos-1yr to match because they didn't have many surrogates available at that time, and the ones they did have weren't comfortable working w/same-sex IP's. I joined the agency and was told to expect at least 3-6mos min. to be matched because there were other surrogates ahead of me waiting to be matched. I was good w/that. Less than a month after I signed w/my agency, I got a call asking how I felt about same-sex couples. I had marked on my application that I was open to it and reminded them. They sent me the IP's profile and I just fell in love w/them! We had a 'matching call'the following week and that was all it took! Significantly less time than both sides were told to expect, but we each met the requirements of the other and it just clicked. We were officially matched the end of April and transferred that Sept. In between we had contracts, them picking out an ED, syncing cycles and then ready for transfer.