To remove the broken drill bit you will probably have to remove the head and take it to someone to spark erode the drill/stud out.
My R1100S has the same two stud arrangement as the 1150gs and has happily run with just one stud up until recently when I finally got round to fixing it.
Having said all this, you can often find a complete head on ebay for a reasonable price and swapping them over is not a huge job.
Edit, don't know what side or year your bike is but for example:
http://www.ebay.co.uk/itm/BMW-R1150...pt=UK_Motorcycle_Parts_13&hash=item19de8d5848