You shouldn't have to dine alone--unless of course you choose to. I would suggest requesting a large table. They usually put at least a couple of solo cruisers at large tables so they are not uncomfortable about being solo. From what I've observed, most couples go out of their way to include the singles in dinner conversations and make them feel comfortable.
I have cruised at least 10 times solo and love it. I find it very relaxing but have no trouble making friends. I often spend time time talking to the crew, bartenders and get lots of good information. I ask for a large table and as f-mattox says, the cruise will try and put you at a table with other solo cruisers. I look forward to dinner and sharing our day together. A Transatlantic would be very interesting for me, I hope you enjoy yourself too !
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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.
I've sailed solo a few times and absolutely loved it. You can do what you want, when you want, without having to worry about someone else's priorities. I love meeting new people, and have always sat at larger tables for meals. I've met people on excursions, too. That way you know you have something in common. You'll also meet people, if you want to, at organized activities. I had a ball at some trivia games, and pool games. I've not sailed on Seabourn, but would imagine, you will get to know more people since the ships are smaller. I hope you have a marvelous time. Please let us know how it goes when you return. Best wishes!
I used to always sail solo and absolutely LOVED it!!! Freedom to eat and drink where and when I want. I don't miss the single supplements but they weren't that bad. I used to frolic about in my room and balcony but, after the whole Erin Andrews debacle, I think that I would be a tad more conservative.
Meeting other solos at dinner is always a hoot. The vast majority of solo cruisers I have encountered are extreme extroverts. They love conversation and are rarely uncomfortable in any situation.
There are some events for single cruisers (whether that's single as in marital status or cruising alone) like lunch and trivia. Your dinner table will have other companions so you'll meet people there. You can also meet people on excursions or at the pool.