I don't have a bachelor's degree at all (I have an associate's) and I am working as a professional software developer for a startup, so yes.

I recommend you do some freelancing as it's potentially the easiest way to break into the industry in your situation. Look at markets like http://guru.com/ and see if you can find projects that match your skillset.

Build up a bunch of five star feedback, and then start applying for full time positions (if that's what you want) with your freelancing profile as your portfolio. Worked for me!

(Note as some others have mentioned, however, that you will not be able to work for a top software company like Google or Microsoft as you will be instantly filtered out for lack of academic qualifications. Your only real path into one of them is through an acquisition.)