Can goldfish be happy on their own?

I have a comet goldfish called Bilbo she has been on her own for a while now firstly because the fish that was with her got fin rot (about 4 motnhs ago)so we immediately took her out and put her in another tank so she never got it. We got a better tank after this with a filter and a light... and thought lets get another fish ( 1.5 months ago) ... we did got a Shubunkin which seemed happy enough till one day it died ( 3 days after getting it) my fish bilbo swims around like a loony digs at the gravel and eats like a horse!! She seems happy enough going in and out the ornaments and picking at the plants! Just don't want her to be lonely but also don't want to get another fish for it to die aswell am thinking she may be territorial now after being alone for a while?