Yes, singing can be taught, but first, do you really want to sing? Eighteen years playing and you're only now thinking about it? I'd bet you have some friends who are pretty good singers and you are somewhat embarassed to go for it(?).
You only live once - GO FOR IT. There is nothing more fun than singing with friends. I think Homespun Tapes (Happy Traum - Woodstock) has a few taped lessons on singing. That might save you some bucks.
The really fun part is learning to harmonize. If you have a deep voice, you can add a lot by singing bass (when singing with others). If you have a higher voice, perhaps tenor is the ticket. If you don't want to fool with all that stuff, that's okay. Just start singing with others. You'll pick up a lot by just doing. The best training is OJT - or maybe in this case, WGS (With the Group Singing).
Good luck!
Jim