、。
Mother is about to take a bath.
Literal
Mother [topic-は], bath [in-に] enter-intend is-doing.
The volitional form 入ろう + としている expresses 'is trying to / is about to enter the bath.' Without しているthe meaning would be 'decide to enter' or 'intend to enter' — the auxiliary puts it in progress, locating the action on the cusp of happening. Useful for the English 'about to' sense that a plain present can't easily convey.