Going with some hesitation to make a bid (5)
I believe the answer is:
offer
'make a bid' is the definition.
(I've seen this in another clue)
'going with some hesitation' is the wordplay.
'going' becomes 'off' (I've seen this in another clue).
'with' means one lot of letters go next to another.
'some hesitation' becomes 'er' (sound made while hesitating - um, er).
'off'+'er'='OFFER'
'to' acts as a link.
(Other definitions for offer that I've seen before include "Sum of money proposed as payment" , "Tender for acceptance" , "Provide (an opportunity)" , "Proposal; reduced price" , "Make available for sale" .)