Hi Christine ...
The OFHS's Oxfordshire Marriage Index (1538-1837) confirms the marriage:
06 JUN 1804 - Mary BATES (of South Weston) to William BEEMSLEY at Stoke Talmage
Note the slightly different spelling of the groom's surname. The actual parish register entry may give names of witnesses (and possibly other information) which may be of use. Although Mary is recorded as "of South Weston", this may only indicate her residence at the time of her marriage, NOT where she was born.
As you have an approximate birth year (1782 - from her burial record), it may be worth contacting the OFHS to request a look-up of their Baptism Index - see "Search Services" on their website at www.ofhs.org.uk