I don't think they print conventional service manuals any longer so you won't have much luck to find a standalone PDF.
Since 2007 BMW publishes a global DVD that contains most (all) of its model. It's called "RSD - Repair And Service Data BMW Motorrad" and is used mainly by the dealer network. You can find copies on ebay. It runs on Windows and you can browse the model you want and the chapter you need information on.
The copy I bought (dated Dec 2016) includes the G310R. You'll have to find a more recent copy obviously to get the 310GS data, might require a little patience before they pop out on ebay.
Can always ask the dealer what's the possibility to get one trough them but I suspect if they can sell to end-user that the cost will be much more than the $13 ebay copies.
What you need the service manual for?
You have a three year warranty :grin2:
Tinkering or repairing?
All kidding aside, I too am waiting for one on the GS.
Just like to have the details on my motorcycles handy.
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