Agouti, of which bay is a variety, is a modifier. It restricts the production of black pigment off the body and face of the horse. As such, agouti can be carried by red based horses, but does not express as they don't produce black pigment.
White and cream are different. White is a result of a patterning gene (true white, as in white markings, not grey which is a modifier). Cream is a dilution gene - it dilutes the colour of the horse.
There are only two "base" colours - red and black.
ETA: This is what happens when you leave a reply window open for ages, you say the same thing as ND