I've been trying to find a HRM that isn't a royal pain that will do that.
One to look at is the Suunto T6. Tons of features, complicated, not sure about
the software. Polar makes a couple cycling oriented HRMs, lots of features, complicated, software. You may wind up doing a dual boot, so you can use the software. There may be a way, but I have never played with Linux.
I like those Garmins, but I mostly use a HRM in the winter and off the bike.
I think I'd feel a bit silly using a Garmin on a trainer.
If you want a cheap way out... I have a SI Fit 3 and like it. It beeps if you go out of zone, above or below. You can guesstimate your time in zone easily.
They also have the Fit 7, which may be even better, but I haven't used it.
The Fit HRMs, are NOS, they've been sitting around for years, and will need batteries either right off or not long after you buy it. I found it easy to use and
sufficiently versatile that I didn't mind.