X-rated Bob wrote
Find the position where it intonates properly. Thereafter change strings one at a time.
Setting the intonation is fine, the problem is really that when the strings are on, their most natural way to rest would be as straight as they can, and when I bend strings upward, the bridge gets pulled up into a place where the strings are at their straightest, the problem is that at their straightest, they're not inline with the neck and poles correctly.
Alan Ratcliffe wrote
Q: if you pull the bridge slightly to one side or the other, do the strings line up with neck and polepieces?
If they do, then you just need to reseat the bridge, which is a fairly common thing on that type of bridge. I use sticky sandpaper stuck to the top of the guitar, then just move the bridge back and forth between neck and tailpiece over the sandpaper to reprofile the bottom of the bridge to the top.
The other way to do it (especially if the grooves in the bridge are badly spaced is to file the top of the saddle and recut the grooves.
You can't do much about a rocker bridge rocking though. A lot of guys used to replace the top part of the bridge with a model with roller saddles (Schaller IIRC), but that does change the look.
A: When I move the bridge slightly to one side for the strings to line up with the neck and pole pieces properly, the strings don't seem to be at their ideal resting place, which is why they then get pulled into their ideal resting place when I bend upwards.
I think what I need to do, is when I put the strings on, is to have them come over the bigsby's string bar slightly to the right of their anchors so that the strings will pull the bridge into the correct position. They come over pretty much exactly ontop of their anchors at the moment. I've not had this issue at all before, it must just be that I restrung it poorly.
It's worth noting that my Electromatic's bridge rarely moves when I put pressure on it, the 6120's seems to be particularly slippery on the top of the guitar.
EDIT:
Thanks for the help, I've moved the strings to the right of their anchors as they come overs, this seems to be leaving it in place. Sorry for wasting your time!