The hex opening on one of the bolts on My Ultregra crank arm is stripped. How do I remove the bolt?

EZ outs in a drilled Hole in the end of the bolt.. go to an auto parts shop to find one . it gets tighter as you turn it CCW.

The classic recommendation is to find a Torx bit that's ever so slightly larger, hammer it in, then undo the screw.
In those dimensions, I've never had much luck with the reverse-thread extractors.

You could epoxy a sacrificial hex driver into the recess.

I had success by carefully filing some wrench flats which were then held by a vice.

For the record, EZ-out-type extractors work great on small bolts; most people (who don't know better) don't drill them deep enough (they require a depth of at least 1/3 the length of the spiral for reliable use), or don't center-punch the broken/stripped head before attempting to drill it for the extractor. The second important bit is that they are intended for bolts whose heads are beyond use of a short extractor like one of these. Hex socket bolts are a best-case scenario for the type linked, requiring little, if any, preparation.

But before that, are you referring to an 8mm socket, or one of the modern 5mm opposing designs? If it's the former, you'll have to use a regular (large) EZ-out to fit the socket. Again, they work fine, but if you need to run out to buy an EZ-out, a [large] tap handle, center punch, and appropriate drill bit, you may be better served bringing it to a trusted shop, for the amount you'll wind up spending.

Take a cold chisel and bang a notch into the outer circumeference of the bolt. Then put the chisel in the slot at an anglew so that when you hit it, the bolt will spin counterclockwise.

Is this a pinch bolt on the crank arm or a chainring bolt? If its a chainring bolt, just drill it out. Its two pieces threaded together and you only need to drill out the inner piece to get it out.

Post a photo. I think there are quite a few different bolt designs and it will help everyone get on the same page.

Some recommendations for steel stuck in aluminum include welding a tool to the bolt. I've always found it to be a scary prospect, but still worth considering.