Bill could be one in river astride swans (7)
I believe the answer is:
expense
'bill could be one' is the definition.
(a bill or invoice is a type of expense)
'river astride swans' is the wordplay.
'river' becomes 'exe' (River Exe).
'astride' indicates putting letters inside.
'swans' becomes 'pens' (pen is a kind of swan).
'exe' going around 'pens' is 'EXPENSE'.
'in' is the link.
(Other definitions for expense that I've seen before include "Disbursal" , "damage" , "What something costs" , "Incurred cost" , "Cost - price" .)