Why Yorkshire? And are you certain he was a convict ? Where does that info come from?
The marriage record says that he was a widower and was free at the time of marriage. The marriage was in 1835 not 1849.
The Tasmanian convict records have only two William Sidebottoms both transported in 1825
The first was transported on the Medway arriving in the August of that year, the records have his place of origin as Newton Lancashire.
https://convictrecords.com.au/convicts/sidebottom/william/110974 says this man was an Ostler, he was 50 when transported so would have been 60 at marriage, thus born long before 1806.
The second was transported on the Medina, arriving in April of 1825. His given origin on some records is Islington, Middlesex (London) but that may be where he was at the time of his crime.
He was younger with a birthdate on some records as c 1805 but others as late as 1809 so perhaps more likely to be your man.
There is a lot of info available about him but a lot with conflicting information and at least one alias, a jigsaw that needs piecing together.
Digitial Panopticon has links to many records and the plot definitely thickens about his possible birth place with both London and Manchester on documents. He also used the name James Sidebottom.
The Digital Panopticon William Sidebottom , Life Archive ID fasai64020 (https://www.digitalpanopticon.org/life?id=fasai64020). Version 1.2.1, consulted 20th September 2020 If you click on VDL founders and survivors you get a detailed breakdown of the sources used.
If you click on each talis link it takes you to the record ( I don't think all are freely available.)
Crucially he was freed in 1831 so free in 1835 for the marriage.
Another Digital Panopticon record appears to be for the same man. ( this is the British 'side'. It has links to the account of his trial and transportation)
One researcher has left information on this William Sidebottom at https://convictrecords.com.au/convicts/sidebottom/william/110862 .His research suggests that the man may have been born in Cheshire. If you think this could be 'your man' I would redo his research.
But unfortunately no sniff of Yorkshire.