Does dressing room cause the "sending too many messages" filter to activate like Outfitter does?
There are 8 sets.
Each set allows you to name the set and to the right is an icon. If you hover over the icon it will provide the keystrokes to switch or save. I believe Shift-Click on that set Icon will save your current gear. Similiarly there is a sword like icon to the right of each Skill Bar. If you Shift-Click on the sword icon, your current Skill Bar will be saved. Two bars are provided per set.
In the lower left corner of each set is a box with words in it "Set 1", "Set 2", etc. If you click on that then you switch to both the gear and Skill Bars for that set.
Hope that helps.