i just push the heater hose on the shaft -- it usually is a real pain to get on and i don't have any problems with them slipping.
as far as the bearings turning i have never had an issue there unless i tried to run the drum with nothing in it. an empty drum won't spin.
fill with at least water to test the more weight the better it turns. good luck any more questions feel free to ask.
After reading your comments and Babaganoosh's about having a hard time getting the hose on the shaft I looked at the hose closely and it says gas line on there and not heater hose. Looking at the inside of the hose it is very smooth so I wonder if the heater hose that you guys put on has a rough surface. Anyway I sprayed some glue on the shaft and inside the hose and that took care of that.
The bearings were a little stiff to move even off the shaft so what I did was remove the front shaft and bearings. I put the tumbler on my wooden table and on a piece of 2 x 4 I installed 4 wheel rollers the same position and height as the shaft would have been. I put the drum on and let her go and it is working perfectly. I ran it for about 18 hours cleaning some brass.
This morning I took off the rollers and switched the back driven shaft to the front and put the front ones back on in the rear position and mounted the pulley on the back again. So basically I have broken in bearing up the front now and the rear shaft wont matter because it is being driven. I fired it up and away it went. So it just needed the bearings to be broken in so when you go to the store, try the bearings and see how hard they are to move without grease in them. Mine were not that hard to move but it still didn't work till they were broken in.