Gents,
I should apologise for the brevity of my post this morning.
Phil.p is quite correct, you can anneal copper by heating to cherry red then quenching in clean cold water. BUT, as per my apprenticeship (many moons ago!) this could have the disadvantage of setting up stress cracks, particularly if the copper concerned was not evenly heated and/or evenly cooled (likely to be the case dealing with a length of copper pipe/tube). Cracking can also occur if the pipe is thin-walled, which I thought may be the case because the pipe Myfordman is trying to bend is quite a small OD.
The advantage of quenching in clean cold water is that any black scale deposited on the copper as a result of heating to red tends to flake off easily after cold water quenching whereas if allowed to cool naturally any scale can be a bit of a PITA to clean scale off (IF there's any present - that depends on the flame and how close to the metal it's held).
As someone else has said, if you "bash it around a lot", copper will work-harden quite quickly so it's a case of having to anneal several times if you're working the metal a lot. But I wouldn't expect that to be necessary if it's "just" a question of making one bend. But if it does start to harden half way through bending (you should feel it start to become suddenly much more difficult to do the bend) then anneal again.
As others have said, bending springs (internal or external), dry fine sand, or Cerrobend should ensure that the inside wall of the bend doesn't "kink inwards" while bending. Another trick is a length of soft iron wire if it's a tight-ish fit inside the pipe, but do leave enough wire length to be able to get a good grip with pliers or something to get the wire out again. (DAMHIKT!)
In all cases, anneal before starting the bend, obviously. And as above, take your choice between cold water quenching or air cooling when annealing.
Hope that helps and sorry if I was too brief this morning.
Krgds
AES