I pulled a Time Out camper behind my Gold Wing and then later pulled a Kompact Kamp Mini Mate behind my ST1100. The Mini Mate is a bit lighter than the Bunkhouse but I'm sure it will pull just fine and the ST, either one, has plenty of grunt to pull it. Just remember that your stopping distances will be a lot longer as will your acceleration be slower. It is very likely the only time you really notice the trailer behind you is during those times... and also if you happen to ride over some really rough road where the bumps that the camper wheels ride over are somewhat amplified through the bike frame. But on smooth roads and at speed it becomes almost invisible. Definitely take care with load distribution and pack the trailer so there is about 30 lbs weight on the tongue/hitch coupling (maybe a few lbs more more since the Bunkhouse is heavier overall). You can experiment with that a little higher or lower to fine tune the ride. I used a fish scale to measure and found that for me my camper rode best with 26-27 lbs tongue weight. Make sure the load won't shift once you have it all placed to achieve the tongue weight you want. I also tried to limit what I put on the bike when I pulled the camper since everything I needed fit in the camper and less packed on the bike improved handling. I only kept what was essential, tire plug and pump kits, rain suits, tools were about all I packed in the bike saddlebags. The top case was kept empty for holding helmets when stopped and there was plenty of room in both to hold groceries if I stopped before arriving at the campsite.
Sometimes I think I'd like to start pulling a Mini Mate camper again... but then I really don't camp as much as would call for spending that much to buy a camper and hitch.