From Hiiperton the canal is probably a good route, it can get very busy with pedestrians and dogs around Bradford but should be okay at that time. I would avoid Brassnocker, it gets very busy with commuter traffic going into Bath and can build behind you especially on the bends (it's also a pig of a hill). There is a road further along called Claverton Hill, this takes you up past the American museum and the Dogs and Cats home right into the university. To get to this you could come off the canal at Dundas Aqueduct and get on the A36 toward Bath but this is a busy road. I've not done it on the bike but there is a small road (Ferry Lane) that I think you can take from the canal if you continue along past Dundas about .5 miles, take this up to the A36, turn left toward Warminster and then take the first right (I have a feeling there's a couple of stone pillars either side of the road) and then just keep going up.
I think other alternatives would involve quite circuitous routes such as taking the cycle track from Dundas along to Monkton Combe and then using the new tunnels, up the Wellsway and then back along through Combe Down, this would probably add a 2 or 3 miles. Another option would be to stay on the canal and get off closer to Bath and head up Bathwick Hill (busy but wide) but again this puts a few miles on your journey.
Good luck