at least tit might be quite dimensionally stable.I love working with vintage wood that sat around 100 years. Of course it's wood, so it grows and shrinks but I find that wood also shrinks on a permanent basis for quite some time but reaches a point eventually where it basically stops contracting. one technique for identifying if an antique is fake or real is to look at wood shrinkage over the length of parts as a counterfeit antique will not usually replicate that less obvious shrinkage detail. wood shrinks more across the grain but you can note some reduction of length in 100 years. I tend to think that it does reach a point of equilibrium.
If you cut it then you do release the internal stresses and may see it still move and normalize but at least better than working with wood that's too green.
the grain pattern is important so your bat may not be the best piece you can find so far as being straight grained etc. If that is the property you are most after.
Ash is often used for axe handles etc. it has some characteristics. lots of nice snooker cues are ash. I agree its not the most pleasing grain so far as cosmetics. . they dont make axe handles, bats, hammer handles, etc from ash because of the way it looks but because of it's other inherent characteristics. It has good shock resistance. It's cells are open so it isn't good for outdoors and to finish it you may need a sealer. It might be more suitable as a shaft than as a butt because often you want the butt to look beautiful. My thought is that the shaft material is more about function than beauty. Obviously you aren't making a full length cue from a baseball bat.
the shaft of my cue is ash. the cue is straight and works nice , the grain pattern could be more straight and there is one spot that had a bit of a defect. I just filled it with wax and it's ok.. If I had the choice I'd look for a shaft that had a bit more concentric and straight grain pattern. i think it might be more common to find those long straight sections of maple than ash. really you want the trunk and not some chunk from near a branch where the grain is wiggly. you dont want the trunk to be curved, you want a straight section of the trunk. the straighter the grain is the more likely it is not to go all crazy .
if Im making furniture , Ill try to pick well seasoned wood and then sometimes trim close to the dimension I then wait and let it sit a while, then make my parts to final dimension, it will move more after the piece is sectioned out and takes some time to normalize.
I think cue makers do similar and also use selectivity, chuck the ones that move too much knowing they will move more in time. selecting the ones that don't move over the less stable pieces.
often what I will look at in my selection process ( I don't make cues), is the end grain. looking from end its easy to see by the arc where in the tree it came from. you will usually see the arc ((( pattern. you know the ( left side of my diagram) is the bark side. if you cut a plank from that like this I(((I then you know that as it dries it will go towards the cup being towards the left hand side. what happens is the grain structure is different towards the core of the tree than the outside of the tree. . the way I remember which way I know it will cup is by thinking that "the arc will straighten". thats not true really, just a way to remember which way..
this might not be of much help in cue making but it may come into play if you are doing sectional glue ups. if stresses can be opposed then they tend to equalize. its common when making a tabletop to alternate them so that top doesn't develop warp.
Where this is more obviously important is something like building a staircase. because you can predict it , if you place each tread bark side up then it will cup upwards. if it cups upwards then it becomes like a dish , holds water, the nails will pull because the plank rocks. your staircase won't last as long.
if the other way then the cup is downward, water runs off better, the plank won't rock so much. you can also see by the size of the arc , how big the tree was that it was cut from, big tree, less arc.
If you find a plank in the stack that has a grain pattern more like IIII as viewed from it's endgrain that piece is more dimensionally stable.
a sawyer has a choice when cutting wood, to select the sequence of his cuts, he may choose to try to cut it quartersawn or to simply slice it up.
if you visualize the trunk sliced , you will have pieces of varying arc but that one in the middle has a grain pattern that is more equal. the center of that plank may be punky, the core of the tree is sometimes susceptible to bugs etc, but aside from that it may be really nice there. to make a cue you don't need that wide anyway. If the tree is cut like a pie then that's a lot of wood waste but the planks will be more concentric and thus more dimensionally stable.
Where this may help you is not with the baseball bat, but when you are at the lumber retailer looking for your perfect piece that is the more dimensionally stable one in the stack. look at the end of the pile, there you will get a good picture of where it came from in the tree and a good selection there will help it warp and move less. knots mean instability, but also more figurative and beautiful grain. you may want those figurative pieces to admire their patterns , ribbon etc.
Your bat probably already has the identification label and I believe they put that label on the side that reflects this. you may be able to identify which side that is by looking at it from end. is that label on the bark side or the other side? It's designed to take the impact of the ball and has some spring to it, the grain maybe chosen with this in mind, A pool cue is designed to stay straight and resist warping due to humidity changes. you might want figure and beauty as well as function. Both are things to consider.
I'd just say it's your art and your decisions I thought the detail about grain and movement might help you or some in the selection process...its all stuff to consider. I know it was more than you asked for in the question.. Hope it wasn't too far off topic.