A bay, bred to a horse with no spotted/pinto/roan/dilute gene, can only produce chestnut, black, brown or bay. Spots/pinto/roan/dilute genes then affect that.
This mare is 50/50 for red factor, with a red parent and a black-based parent. SO, 50% that she's going to produce a red-based foal, which is then affected by probability added by the sire whether it'll be with spots, pinto, roan, or diluted in some form (dun, champagne, creme or pearl). Then the other 50% is shared between black, brown and bay. I can't remember if brown hides on bay or not but bay and brown are two forms of the agouti gene.
I'm not really making a huge amount of sense but I can't explain any more without knowing the colour of the prospective stud.