ALmost certainly not bay unless the mare carries bay and isn't showing.
chestnut is recessive to all things
bay is dominant to all things but only expresses in black horses (It's a modifier gene that restricts black to the points). So your black horse doesn't carry bay, but may carry chestnut
so most likely is either chestnut or black
maybe bay
white markings are way, way too variable to be able to predict. Best you can say is 'might have white socks/blaze/abdomen'
many years ago before all that genome stuff the owner of the riding school I went to put her black mare to a liver chestnut stallion twice and got a pale "pink" filly [never before or since seen anything like it!] and a darker chestnut filly. A bay mare who went to the same stallion produced a red chestnut filly...
Apparently she was hoping to get a bay... never could figure out how she thought any combination of black/bay/liver chestnut would produce that tho'
She did eventually send the bay mare to a bay stallion and got her bay colt!