One getting up only a bit of the stairs (5)
I believe the answer is:
riser
This clue is a double definition.
'one getting up' is the first definition.
(one rising or getting up)
'only a bit of the stairs' is the second definition.
(part of a stair)
(Other definitions for riser that I've seen before include "One on the way up" , "One getting up" , "He gets up" , "Vertical piece between two steps of stairs" , "Front of a staircase step" .)