I've got a similar setup (no highline though) and bluetooth part numbers 5K0 035 730 & 7P6 035 730 will work with the RCD510. It all works through the Touchscreen but won't talk to the Highline. These units work with all phones unlike some of the other VW units that need an RSAP phone.
There can be some problems with the phone book transferring into the RCD510 - seems to depend on which version of the RCD you have. I found with mine that 5K0 035 730 B worked best with my stereo which I think is quite an early one.
I was going to stick a 7P6 unit in the for sale area tonight
