I always go to bed at 10.

Literal

I [topic-は] always 10 o'clock [at-に] bed-attach.

床につく ('to go to bed') is a slightly literary set phrase — literally 'to attach to the bed/floor.' 床 here is read とこ (bed/sleeping area), not ゆか (floor). More poetic than 寝る ('sleep'). に marks the time point at which the action happens.