Yes there is a bleed sequence. Unscrew the adjuster screw that can be reached though the hole in the red ring that says "FRONT", REAR and OFF". Slacken it and then pump the handle until oil starts to come out of the little hole nearby. Then retighten/lock off the screw again you have just bled the system. What a marvellously high-tech item this is!
A gasket pattern for front cover of pump - a PDF file
This article was initially written in 1941 and although it mainly refers to the Smith Jackall system as fitted to the MG SA, WA and VA the general principles also apply to the system fitted to the MG Series Y.