Lawson's iron wire that everyone is mentioning is a nice line. I have some that I use on tents, packs and other things, but admittedly have not used it as bear line, but think that it would do fine.
I had been using the 1.4 mm slick ZLine from ZPacks for a while and it did great. However, due to it's tiny size you have to be very careful when raising or lowering the bag...if it gets away from you, it will wreak havoc on your hand/fingers, of course, any line will do that, but this line is tiny and can be hard to hold. I always just wrapped it around my hand a few times and then simply walked away from the tree to hoist the bag up, or towards the tree to let it down. Also, this tiny line can cut into tree branches if raised or lowered much, so I wouldn't recommend using a line this small for multi day hangs in the same place.
Recently I have been using the HLine that is available from Lite Trail and I have been pretty happy with it. It is a bit thicker so a little easier to deal with than the slick ZLine, however, it also weighs a little over twice as much too...