What exactly does your friend mean by 'best bass'? I ask because it's often not a nuanced or defined sound with most, they just want the boom-boom-boom. That said, closed back solutions are generally going to offer a heavier bass over open back, and of course the environment he intends to use them in will come into play even should he be open to open back and potentially more detailed audio.
Audio-Technica ATH-M50 can be had for around £90 and they're celebrated as being bass heavy, not my cup of tea but would probably fit the bill for your friends needs. Regardless of what your friend ends up buying I'd recommend auditioning when possible, but if not buying from a place with a good returns policy, as the way headphones sound can be very marmite at times.