Not sure if by "the last two centremeters of travel" you mean by the floor or the top of the pedal.
If the clutch is knackered it will let out right at the top, not the bottom/floor. If it is right at the floor then the clutch itself is fine, but if you think it is too near the bottom then you are not getting enough clutch action, which suggests either air, or the slave or master cylinder is knackered.
Bleed it like the guy above says, but if you want to be able to just pump the air out without closing the nipple at the bottom of each stroke, then you have to make sure that you have the tube going into a glass jar which has some fluid in it....then the air will work its way out without sucking it back in again as the pedal comes back up....you will get initial air coming down the tube which you must ignore until you see the fluid coming as well. If the bubbles are large as they come down with the fluid then just keep going until all you have is fluid. If the bubbles are tiny and the fluid in the bottle goes a bit opaque with micro-bubbles then there is likely to be a problem with the master cylinder rubbers or the slave cylinder.
Hope you get round it ok
