Bela + BBB requires no more than 0.5A.
PSU-induced noise will be dependent on quality ... in principle, under-using the PSU may result in less noise than exploiting its capabilities in full, however it may well be that a 0.5A 8€ PSU uses a better design than a 4A 8€ PSU ... who knows (well, the datasheet may, assuming there is one and it is accurate)!