I have found a possible birth, but I'm afraid it only adds more to the confusion. Long Sutton is in the Holbeach Registration District, and in the earlier census, which are likely to be more accurate, her birth year is c1844.
Searching FreeBMD for a Sarah Jane born Holbeach 1844-1849 brought up this for Jan-Mar 1844:
SALTER Sarah Jane Salter Holbeach 14 409
BEDFORD Sarah Jane Salter Holbeach 14 409
The GRO Index only has this recorded once, as BEDFORD, with the field for Mother's Maiden Name left blank. This would indicate that her parents were not married but both were named on the certificate, with the father's surname being Salter and the mother's Bedford.
The 1851 census for Long Sutton shows a
Mary Jane Salter aged 7 living with her grandparents, Robert & Lavinia Salter, along with another granddaughter, Ann Salter, also aged 7.
Searching FreeBMD brings up these two Oct-Dec 1843 entries on the same page:
SALTER Mary Ann Holbeach 14 400
SISSON Mary Ann Holbeach 14 400
Again, the GRO only has this indexed once, under Mary Ann SISSON, with the MMN field blank, but FreeReg has the baptism as Mary Anne SALTER, illegitimate daughter of Jane Salter! To add to the confusion, however, under the same GRO reference there is an Ann KNIGHT, MMN
LISSEN.
Another Salter birth comes up as follows, this time Oct-Dec 1845:
KNIGHT James Holbeach 14 454
SALTER James Holbeach 14 454
Once again the GRO only has this indexed once, under KNIGHT, with the MMN field blank, although FreeReg has the baptism as James SALTER illegitimate son of Sarah Salter.
If you weren't confused enough beforehand then I'm sure you are now!
I think perhaps the best place to start would be the birth certificate of Sarah Jane Salter/Bedford to see if that makes anything clearer!