Using a 2D generalization of Kent's model-independent decomposition method, we extract the K-band light profiles of the bulges of a sample of field galaxies with morphological types ranging from S0 to Sbc. We then examine the shape of the bulge profiles, by means of fitting a seeing-convolved power law of the form μ(r) is proportional to r^1/n^, where the exponent n is allowed to vary. The best-fitting exponent n is found to vary systematically from values around 1 (exponential) to 6 from late- to early- type bulges; the profiles tend to fall off more steeply in the outer parts for the later types. The same trend is seen as a function of bulge to disc ratio. Application of the method to artificial data proves that this result is not caused by disc-light contamination. There are also indications that n becomes larger with increasing total luminosity and radius of the bulge. A similar relation has recently been found for elliptical galaxies. The smooth trend of n with morphological type shows that the formation of or interaction with the disc has affected the density distribution of the bulge.