Breed & color are not the same thing. Knowing a breed can SOMETIMES point toward some assumptions we might be able to make about color genetics, but it's pretty impossible to predict colors and especially patterns, out of some of these crosses we have now. If more people understood some pretty basic rules about color genetics, I think less people would be as surprised (or maybe disappointed) when they don't get what they want or expect or hope to get.
If this cow is solid black and never had a red calf (and even if she isn't "solid black" but black, not red), then there's no reason to think she might have a red gene. Yes...there could be red blood coming from the Maine or Simmental pedigrees, then it's possible that she might, but no amount of white hair, whether it's one hair or most of her body, or roan or spots or zebra stripes, predicts that she might be a carrier for a red gene. The genes that determine whether an animal is black or red are not connected to the genes that determine the pattern (i.e. spotted hides, roaning, white faces, blaze faces, white feet, etc.) You know a black animal is a carrier for red if either (1) she has one red parent, (2) because she has produced a red calf, or (3) because you've DNA tested her. Otherwise, it's a guess, and you're best guess has to be based on probabilities and heritability and everything you know about her pedigree and/or her production.
Unless she's always been mated to homozygous black bulls in the past, and depending on how many black calves she has produced out of red or heterozygous black sires, it seems there might be a decent chance the cow is homozygous black. If that is the case, then mated to a red roan Shorthorn bull will give you a 50% chance of making a blue roan calf, and a 50% chance of a black (not roan) calf. My guess is that, with the Simmental + Maine background, she could easily have some kind of recessive spotting gene, so that might add to the anticipation and the unpredictability of what you might expect.