Hotels in Halong Bay are plenty, and modern now, easy to find when you arrive there.
As for the route, I think we took the QL18 back in 2006, 2-up on a 125cc Minsk.
You have to plan half a day trip to get there.
Best is to buy a vietnamese local road map to find your way out of Hanoi (if you get lost, just ask your direction by saying : "Vịnh Hạ Long" ) and get you into the right direction.
For having done it, going there by bike has no interest whatsoever, the road is pretty busy with many trucks and cars (road to/from China), landscape is flat.
I think the road to Haiphong is as busy as the QL18, Haiphong being the main port in Northern VN.
Better book a 2/3 day Halong bay tour with accomodation through the local travel agencies in Hanoi, and you'll get there on minibuses, arrive in a good shape, have all well organized for you at a not so high cost compared to what you would get by yourself by arguing for a boat in Halong with the locals there.
As for biking, best is to go on bikes to HoaLu, where you can ride around and enjoy the scenery.
Have a safe trip !
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