The new Shimano outboard bearings will work with the Bullseye bb spindle only with the addition of a machined shim...easy enough if you have a lathe, a pain if you do not.
As for new bearings, yes, they are available from many sources on the web. Just grab a set of calipers, measure the outer diameter, the inner diameter, and the width and take 15 minutes to Google and search the online bearing suppliers. I picked up a set for a friend but do not remember the specs... sorry.
Good luck,
rody