BJT voltage noise is the sum of base resistance thermal noise, which is roughly independent of the bias current (at least as long as the device is not in high injection), and the collector shot noise transformed back to the input, which does decrease with bias current. 

The base resistance term is strongly dependent on the transistor type, the collector shot noise term is not, at least not as long as you bias the transistor below its peak fT. (Near and above peak fT, all kinds of second-order effects such as high injection come into play.)

The total voltage noise in V/root(Hz) theoretically equals:

sqrt(4kT*rb+2kT/gm),

with gm = IC/(kT/q),

where 

IC is the collector current
k is Boltzmann's constant (1.38065E-23 J/K)
q is the absolute value of the electron charge (1.6022E-19 C)
rb is the base resistance
T is the absolute temperature

For a transistor giving 0.5nV/root(Hz) at 10mA and T=320K or so, this comes down to rb~=12.76766233 ohm. 

A transistor with 0.95nV/root(Hz) at 1mA, 300K has rb~=41.54731389 ohm, which is not bad, but obviously worse than 12.76... ohm