Much of the GDMBR is open to motorcyclists and has been done on motorcycles. Use caution and have respect for slower moving vehicles/people and that will go a long way.
We did a blog post on the topic here:
Also, if you do an internet search for 'great divide mountain bike route motorcycle' (without the quotes) a number of related links to blogs and forums will appear that can point out the dicey areas.
I hope this helps.