Losing head, refuse bail out (5)
I believe the answer is:
eject
'bail out' is the definition.
(I've seen this before)
'losing head refuse' is the wordplay.
'losing head' means to remove the first letter.
'refuse' becomes 'reject' (rejecting is a kind of refusing).
'reject' with its initial letter removed is 'EJECT'.
(Other definitions for eject that I've seen before include "bounce" , "Spit out" , "Video button" , "Evict" , "Send out forcibly" .)