I hadn't run into this until recently, because I don't use them all that much. It appears they cannot gain levels though. I had 1 with upwards of 100 xps and still sitting on level 1 in the game I noticed in. Is this a bug, or is it for balance purposes?
Regardless a old school bomber with several level upgrades is more valuable than a level 1 stealth bomber imo. I would have thought something like this would have been corrected in last weeks patch if it's not intentional.
A way to deal with the issue is to simply not build any from scratch. You use regular bombers until they have gotten to something nice like logistics or air repair, and then you upgrade to stealth.
Anyways, it looks like it had been reported by someone on the official forum bug thread: