averaging about 12 mph. I ride about 5-6 days a week. I guess I equate faster = fitter. Yes? No? Maybe? Yes.

Is the best way to improve by riding more or incorporate some type of intervals? No, not at this stage.

My main goal for riding is fitness, weight loss, and maybe something like a 1/2 century/century. I joined a local bike club but all of their rides are over 15 mph. Any advice on training? How do you train? - the club ride probably isn't helpful until you can keep up. or they have a social ride which is slower.

My advice to improve is pretty simple, and you don't need any sort of training regimen. Ride every day, no excuses. Try to improve something every time out. Except, when your body objects (knees, sore legs, generally lower energy level etc), just make it a shorter, slower ride. You will improve, slowly but perceptibly, to whatever level you want depending on the effort you put into it.

added:
I work 4 - 10 hour days(my job involves standing 100%). The good news is that it doesn't impact cycling. It used to amaze me that even when I felt dead on my feet, after getting on the bike the feeling vanishes and I could still get a workout. We don't really use the same muscles that got fatigued by that.