I'll preface this with im young, this is my first place out of home and I'm renting so idk how old these lights are

Two of the recessed lighting above the bath have gone out, the plate at the bottom is easy to unscrew and inside is this metal bell shaved cavity with the bulb in it.

There's not really much space to fit my hands in there and whenever I touch the bulb it lifts up, and can be pushed really far into the hole at the top of the bell. It feels like it could go further but I didn't want to break anything.

It is one of those three tube bulbs in both of them and I can't tell what sort of socket it is.

How do I change these bulbs? Do I need a special tool? I need to replace these as my landlord is coming round for an inspection