I've scrolled though the Bastardy Bonds for the 1700's at Ipswich Records Office online and there no mention of Anne. Not all are online, they do have paper and card indexes but I suspect you will have to pay for a search.
Added..
They were both baptised..
James Moss Mortimer
bpt 21 Feb 1796, Ashfield Cum Thorpe,Suffolk,England
Mother: Ann Mortimer
George Mortimer
bpt 11 Feb 1798 Ashfield Cum Thorpe,Suffolk,England
Mother: Ann Mortimer
In the 1841 census there is a James Mortimer b1796 with wife Frances. Living at Thedwestry, Suffolk. Another James b1796 with wife Sarah. Living at Dennington, Suffolk.
In 1851, George Mortimer born c1800 Ashfield, Suffolk with son James. Living at Wetheringsett.