Surface mount or Flush Mount SubPanel

How to violate the NEC...with a bedroom door

Putting the panel "behind the door", as you describe, is actually no good as it causes the door, when opened, to infringe on the NEC 110.26 clear working space for the panel:

110.26 Spaces About Electrical Equipment. Access and working space shall be provided and maintained about all electrical equipment to permit ready and safe operation and maintenance of such equipment.

If you need an example to tickle your imagination, just think of an electrician trying to take voltage readings in the subpanel (thus requiring the situation to be worked "hot" to at least some degree) when someone, unaware of our poor electrician's presence, opens the door to the bedroom right into the electrician, clobbering them into the subpanel box in a most shocking fashion!

So, in any case, I would put your subpanel in the full-width, and fully exposed, adjacent bay instead of trying to "hide" it behind a door.

GO BIG OR GO HOME

There is no sense in using a tiny, six-slot subpanel here; either you're proposing a cutoff for a single appliance (where a "spa box" sized panel is just fine), or you are setting up for an honest-to-goodness feeder-and-subpanel, where six spaces will leave you going back to the hardware store for another subpanel far too soon. Instead, I would go for a 125A, 24- or 30-space, main lug subpanel, given that this is being fed from within the same structure; these often come with factory fitted ground bars, as well as time-saving features such as plug-on neutrals, and will provide ample space for expansion in the future.

Furthermore, if you're really concerned about aesthetics here, there are options:

• Some loadcenter vendors (GE & Siemens, as well as Eaton in their BR line) offer loadcenters with their covers finished in white as a special-order option (talk with a local distributor/supplyhouse for this, you won't find it at the bigbox stores)
• Eaton, for their CH loadcenters, used to offer a decorator cover accessory (CH8KDNx) that could be freely painted or wallpapered to match the room; they don't seem to make it any more for their new CH PoN panels as a catalog item, but there still seem to be some NOS covers floating around...
• Also, if you're willing to do some serious custom ordering (likely with supply house help), Eaton, through their Lincoln, IL Flex Center, offers custom factory paint jobs on any loadcenter in the Eaton lineup.

Of course, if your inspector is OK with having a false cabinet frame around the loadcenter, the "false cabinet door" trick for disguising service access, such as breaker panels, still works, too. (It's pretty much mandatory for the small-circuit Square D loadcenters in this sort of situation, even, since their cabinets don't have a door to begin with.)

Flushmount is the way to go here, BTW

As an aside, you want to use a flush mounted panel here. Surface mounted panels aren't used in finished spaces due to the issues involved with getting cables into and out of them and mounting them securely to the building framing in such circumstances.