Hi cruiselady2, I've been a solo traveler for many years, started out traveling with my children when they were in their twenties, now they're raising families. On the very first or second night, you will get an invitation for a solo get together in one of the lounges by the social hostess. Then they go off to dinner. It happens most nights on the cruise. Like Ngaire said, one of the other staff often hosts these dinners. And you can find cruises with a reduced single supplement under the "special offers" section when looking for a cruise. You'll find more singles aboard when they're offered. Regent used to have Gentleman Hosts on some cruises but that is no longer the policy as I have noticed in past couple of years or so.
As well, at anytime you wish to join others at a table at a time of your choosing in Compass Rose, just tell the maitre d' and he will put you at a gathering table. In the specialty restaurants, I've noticed when making reservations that sharing with others" is offered. Don't be shy...strike up a conversation at any time on an excursion or wherever; join a trivia team with others, go to the various activities on sea days, you'll find that others enjoy meeting new people just as you do! Of course, my kids always say about me, "Mom's always talking to strangers"

. Enjoy!