Have you checked to see that the bellows scale presumes the same CoC as the online calculator? If they have a different CoC, the results will differ. If they don't, you can probably figure out the CoC of the bellows DoF scale by plugging in different values of CoC online until the online calculator agrees with your lens.

If you want a smaller CoC than the bellows scale, you can just use the markings for an appropriate aperture that's a bit more demanding, say shoot at f:16 but use DoF markings for f:11. Use the online calculator to check what the revised CoC is.

I find that on many cameras, I find the DoF chosen by the mfgr to be too loose, i.e. they allow for more unsharpness than I like. So I often pull back a stop or so on the DoF scale, shooting f:16 at hyperfocal for f:11, etc.