If your felxi pipes are 22mm each end then that's the correct size. Reducing the size of the pipe can accelerat pressure but it would take age's for the bath to fill hence 22mm pipes and 22mm taps for dischargindg a larger volume of water.
If you have not had this problem in the past with same set up the I MIGHT be the taps if the same on both. Remove the taps innars [tap heads] clean and coat moving parts with vaselene and replace see what happens. Also look in the remaining tap body, on the bath, at the 'Seating' see if that's clean and free from lime.
Are/is the stop cock fully open? if not open fully but turn back 1/4 turn. (You should operate all stopcocks/check valves periodically to prevent sticking)
Lastly ensure neither flexi pipes are kinked as that will reduce flow.
bob
February 2010