what to do to keep mortar from falling out when placed at the end of bullnose brick?

Answer 1

nothwithstanding the consistency of the mix, if it's just of matter of finishing the job, set the piece in place and cover the end or edge with a peice of masking tape. It will hold the mortar in place until it dries.

Answer 2

In the right consistency, and with the right pressures and clean up engaged in, mortar doesn't recognize Bullnose, from any other block substance.
You don't state if this is happening in the initial application, or after the fact, but mixing the mortar too thin will certainly have some adverse effects, as will not moist enough.
I've "laid" a lot of brick, and all manner of ends, and my greatest issue is clean faces, never mortar not staying where it's supposed to. That certainly suggests,,,again, that possibly the mix was incorrect.

Rev. Steven