Many people don't realise that its actually illegal to grow a plant up someone else's fence or wall without your own support being provided for it. You can get round your problem by erecting a rigid fencing trellis panel against his fence, either by inserting your own posts on your side or, if he is amenable, fixing it to his fence posts on your side. Rigid fencing trellis panels are available in various sizes (1 x 6 feet up to 6 x 6 feet) and I'd recommend the largest. Bear in mind, if he agrees to your using his posts to fix it to, there must be space behind the trellis, preferably about 2 inches minimum, so that the plant can twine properly around the supports.
Keeping your plant rigorously pruned back means you will have few flowers.

Useful and interesting question and answer.
I've added to GoYpedia Climbing Plants :o)

I have a 4X6 trellis ready Bamboo but wondered if it might still be better in a large trough to contain it as my neighbours shed is directly behind the fence .

Susie... you seem such a very considerate neighbour.
Wish you lived next door to me ..... !

If you mean 4 feet high by 6 feet wide, its not high enough - this plant will want to get over 20 feet, so the extra 2 feet of space on a trellis is important. 8 feet high would be even better... You would need to cut it off when it reached the top so it didn't go over your neighbour's shed, but at least it'd have 6 feet to climb up and 6 feet to spread sideways.

I actually meant 6 ft high by 4 wide but I may be able to stretch it out a foot each way :-) So you dont think a pot a good idea then Bamboo ?

My neighbour treated himself at great cost to this run of fencing last year before he retires Terratoonie so I respect that he wants to keep it in tip top condition :-))

Well you can try it in a larger pot, you might get some good out of it for another year or so, but eventually I suspect it'll have to go in the ground. Four foot wide by 6 high will do for the trellis...

Thank you :-)

Has it flowered Susie? I have had one on trellis against a SW facing chimney breast, it has been there 3 years and I havnt had a flower, it will get changed next year for a honeysuckle!