Now, I know it would suppress their power, but how would a Navigator forced into a cell feel, especially compared to a psyker

To be honest with you, there's not much actual information on the effects of a Null bay to a Navigator but I can theorize.

First of all, their third eye would be blind and it would probably hurt them to try and use it.

Then, like other psykers (because Navigators are really just modified latent psykers), they'd have headaches/migraines and other physical aches and pains.

To a Navigator, the psychological humiliation of being treated like a common Psyker and then the shock of being thrown out of their lap of luxury would also play a huge part in their suffering.

Yeah, compared to an "active" psyker, I don't think that the null bay would particularly hinder a Navigator; their mutations a bit separate, and their third eye would stop working, along with its powers, but I don't think they'd really feel it. I also wonder if Eldar, or Orks, would really care. Each is a member of a psychically-attuned race, and each has individuals among it that manifest true power in that field, but they don't count as psykers otherwise, so while they might feel a little off, I doubt it would be cripplingly effective on those who aren't Seers or Wyrdboyz. Also makes me question how a Null/Blank, or a Culexis Assassin, would make them feel, compared to other humans, if they aren't representatives of their races with a measurable Psy Rating.

As said, I could see a Navigator HATING it, yes. If they have a latent connection to the warp all the time, instead of only when training their warp eye to navigate, the loss of that feeling could be very unsettling, and the deprivation of their powers could also be seen as an insult, or even a threat. Being away from what of their resources the individual can scrounge up, aboard ship (not every Navigator is a member of an affluent House, with Scrooge McDuck's vault as their tower) would also suck. Still, there are some Cold Trade types whom I can envision turning a Null Bay into his office/chambers, of a sort, using its effect to block any probes of clients, and suppress any items he has, until they are sold to someone, whose problem now it is. In fact, I might remember that for writing; they are still much easier to acquire than an actual, living Blank.

Consider the following analogy. A "normal" psyker, such as an Astropath, is like a RADAR unit. He broadcasts in waves that rebound from their targets, carrying information back to the Astropath. As such he is visible to demons and other entities of the Warp from the Other Side. Navigators, on the other hand, are more like IR goggles with a laser-painting device attached to their earpiece. The goggles are passive sensors, not visible from the Warp, and gather active sources of sensors that others are employing and relaying that information to the Navigator. Sometime the Navigator decides to take a more active interest (becoming visible to the Warp) and paints a target with the laser (the Third Eye), calling for the standoff artillery.

In this Null case, the Navigator's passive abilities (e.g. Psyniscience) wouldn't be affected, while the active ones (e.g. Third Eye) would be stifled. I'd assume nightmares and headaches would be the norm.