Dear Silvery,
I'm male, but I suspect I've been in the same boat as you find yourself. For many years I suffered from a mild depressive condition. I'm not bipolar (the ups sound like fun!) and it's fairly rare for me to hit absolute rock bottom but a lot of my life has been spent being in a low mood and lacking in self confidence. I've not always been single but my low mood has killed a number of relationships and, if I do become too low, my 'social skills' tend to escape me - not seriously so, but enough, let's say, to make people fail to enjoy my company...
What really changed my life for the better was taking up tango. Seriously, it's a fabulous cure all; It''s good exercise (mildly aerobic, not full on like salsa or ceroc); the people who do it tend to be a bit more mature (30 upwards); they also tend to be fairly intelligent (it's not easy to learn, you need brains to really 'get it') and the conventions of tango are such that you get to meet people for a short, manageable, periods (a typical dance with a new partner lasts about 10mins and then it's over) and so conversation with new partners doesn't become too onerous.
Most importantly - and this is the crucial bit about tango - you get a lovely warm hug to nice music. I actually find it quite meditative, it's the only thing that succeeds in emptying my mind (far better than bloody mindfulness!).
It's considered bad manners (by either sex) to be "on the pull" and only to dance with "attractive" partners - so everyone gets a look in. Lots of singles do it but being too flirty is kind of frowned upon (pervy blokes tend to give up or are thrown out rapidly on their ears by the course leaders - they tend to drive away potential clients). But people do get together and form friendships and even form proper relationships over time. I met my partner (in life) dancing tango five years ago.
If you do get it, it's highly addictive. I've been doing it for several years now and it's taken me to some amazing places all over the UK and Europe.
Unless you're dead set against dancing, full stop, I'd recommend it to anyone as a great way of meeting people in a non-threatening environment and doing something that's both sociable and highly rewarding. I'd go so far as to say it probably saved my life.
I sincerely hope things work out for you.
Tango Hugs
Snot99