just did my 250f bearings, and i bet they are the same, so hopefully can give some tips....
first off is to start with the right tool, i used a socket and a big C-clamp to try and press them out but just broke all the needles out, which left the race in.
local shop had a motion-pro swingarm bearing toolkit which is pretty rad. just uses a heavy duty acme thread, with perfect-fitment sockets on each side, then you just use an impact wrench to drive them out. i tried my C-clamp with a breaker bar and it didnt budge the bearings out.
got lucky that the tool pressed the broken bearing out without scarring the inside of the swingarm bearing mating surface.
a press would work well too.
going back in, stick the bearings in the freezer overnight, then heat swingarm area with a torch a bit, will have to work fast with the bearings cause they will warm up fast and slow down on how fast you can press them in.
on the 'how far do i drive them in' question, check out this drawing, its probably similar to yours.
http://www.kawasakipartshouse.com/oemparts/a/kaw/500b6e96f8700223e47980fd/swingarmon the outward facing direction on the opening, you see it steps down. so the area the bearing sits in is actually a smaller diameter than the outside area with the seals and collars.
i used an old collar, part #92152 in that diagram, to help push the new bearings in, what this will do is let you push the bearing down to the correct depth by letting the collar to not push in past the lip of the deeper area if that makes sense. so when you cant tighten anymore, then the bearing face should be flush with that lip, thats proper bearing fitment. if you used a socket or something that was same size as the outer diameter of the bearing, then you could push the bearing all the way thru to the other side. but with that collar, it will only allow you to press the bearing flat to that face, right where it should go.
hope that wasnt confusing.
and make SURE you are straight with the bearing as youre starting it. i usually sit it flat on top. then gently tap it with a mallet until it gets started, then press it in a bit by hand with a clamp, then move on to a press. thats being paranoid, but if you press that thing in at an angle you can warp the bearing and scar up the surface.
