Thanks JayJay. Any chance I could pull the old one and clean it and replace it, and hopefully have it work? Not being cheap but my dealer is 50 miles away and a trip in and back will surely kill most of a day.
Well, if you don't try you'll never know. Just be real sure to get it dry before you reinstall. Any water in that system is a big huge no-no.
I haven't pulled a bleeder valve in quite a while, but IIRC they are a shaft with a tapered end to fit into the seat. They are hollow most of the way down with holes drilled in the side of the shaft to connect with the hollow core. When they're tight the tapered part sits in its seat and holds pressure. When backed off the fluid can escape between the seat and the tapered end, thence through the holes and up the shaft. So I'd look to the quality of the seating surfaces in both the seat and on the bleeder valve.
BTW, you can always mail-order a replacement if cleaning doesn't work.
Just be careful about tightening. If the seating surfaces mate up correctly it shouldn't take much torque to seat them - snug plus a micro-skoche more. I don't remember the spec but I would guess around 6 Nm. Too much torque and you've stripped the handle, and then you will either have to put in an insert or replace the handle. And I don't imagine those are cheap.
An alternative suggestion - if you haven't changed your brake fluid in a while, this might be a good time to do it. BMW recommends every two years. If it's time and you don't do that yourself, take it in and tell the dealer to check out the leak.