Well, first of all, it's very common for them to go off their feed when shedding, and when they've recently come into a new environment. So I wouldn't worry much about the low appetite just yet. If it doesn't improve within a week or two you may want to have its poop tested for parasites, but even that is still within the possible time period for relocation stress. Some dragons take longer to get over it than others.
Also, what do you mean "all three bulbs"? As far as I know a beardie really only needs two bulbs -- a
UVB bulb such as the Reptisun 10.0 or the Arcadia 12%, and a basking bulb, which can be any clear household bulb provided it produces the right amount of heat. If your home does not go below about 70 degrees at night, you don't need any kind of night bulb or night heat at all. If it does get below that, the best thing to use is a ceramic heat emitter rather than any kind of night light or night bulb. Contrary to what the people at the pet store may tell you, beardies can see color, and therefore red nightlights and blacklights are both inappropriate for them. They can see the light just as much as you can.
How often does he have his eyes closed? It's normal for them to nap or doze a bit while basking but if he's keeping his eyes closed a lot then it's possible his eyes are being burned by your
UVB bulb if you're not using one of the two brands I mentioned above. ALL other brands are generally inappropriate for beardies, unfortunately, and some can even cause damage to them.
If he is constantly basking and never wants to come down, your cage might be too cold for him. Or else he might simply be feeling overwhelmed by his new surroundings and just wanting to hang out where it feels warmest and safest right now.
Also if you are giving him daily soaks there is no need to mist him in addition to that. Dragons are desert animals and do not need to be kept moist.
Bathing is good for them, but they do not need misting. Some people choose to mist INSTEAD of
bathing, but I prefer
bathing, personally. You should give him soaks even when he is not shedding, though they can be every other day if you wish. I give mine daily soaks because they both prefer to poo in the
bath, and it's much easier to clean up there than in their viv or anywhere else they might go, so I encourage this by
bathing them every day first thing in the morning after their initial warm-up bask.