I sailed solo on Seabourn several years ago, and it wasn't a problem. The staff is very aware of people traveling alone, and make it as easy as possible, especially at meal time. I found invitations in my stateroom almost every evening, to join different tables for dinner, usually with an Officer "hosting" the table for the evening.
After a day or two, you'll meet folks onboard, at various activities or just enjoying the ship, with whom you may want to eat dinner. Or just showing up at the dining room for any meal, and being seated at a table is a great way to meet people. The ship is small enough such that you'll see these people over and over again, and see a lot of familiar faces before too long.