A power bleeder will make your bleeding process much easier, especially if there is trapped air in the system that you cannot get out. It may not be a bad idea to invest in one:
Mini Cooper & Cooper S (R50/R52/R53) - Brake Hydraulics - Page 5.
Also, not that this is your issue, I'd check your shift linkage and make sure they're not damaged/corroded. If those bind it can cause shifting issues, but your issue sounds like it's more likely related to air in the system or something else.