Bastardy bonds are a feature of the Old Poor Law (pre 1834). What you are looking for in 1854 is an
affiliation order. If the mother applied for such an order she would go to the petty-sessional court for the district where she was living at the time of application. This is not necessarily the same as the child’s place of birth. She had to apply within 12 months of the birth.
Returns of such orders were also made to the quarter sessions. Have you look at the returns catalogued and name-indexed here (up to 1857)?
https://somerset-cat.swheritage.org.uk/records/Q/RCB/2If you find something here, you can ask the archive to quote for sending you a copy.
If the family was not well off, you should also look at any surviving records for the relevant
poor-law union (e.g. guardians’ minutes). These aren’t usually online.
Otherwise, there may have been a
voluntary agreement between the mother and the father, and a record is unlikely. Or there may have been no support at all from the father.
As a general rule, if you can’t find something online,
email the county archives with the details and ask what they have that might help your search. This sort of general enquiry is normally answered free of charge.