Hard to tell from the pics, but sometimes you can use a suction cup to grab the bulb and rotate it in and out without removing the trim rings from the fixture. Also, in most recessed fixtures, the baffle and outer trim ring are two separate parts. The inner baffle usually just fits to the trim ring by friction, but sometimes with springs connected to the can. Guess you won't really know until you get first bulb removed and get a look inside. You should however be able to remove the bulb without taking the fixture apart.
If you can't find a suction cup, try looking for those little 1 or 2 inch suction cups with a hook attached, like the ones used to hang decorations on a window etc. These cups are often included in the bulb package of some types of small bulbs like GU style. Good luck.