If you use a decent transcription, for example
https://freecen1.freecen.org.uk/cgi/search.pl, there are the following references to an Ann(e) Pringle born in Bedrule
1861, Ploughman's House, Morebattle. Robert Pringle, 46, born Eckford; wife Ann, 48, born Eaton; children including Ann, 22 born Bedrule.
1851, Lempitlaw, Sprouston: Robert, 36, born Eckford; wife Ann, 38, born Ayton; children including Ann, 11, born Bedrule.
1841, Lanton, Jedburgh: Robert, 24, born Roxburghshire; Anne, not born in Roxburghshire; children including Anne, 2, born Roxburghshire.
FindMyPast also transcribes it as Bedrule.
So it looks as if Ann(e) was indeed born in Bedrule, in 1838 or 1839.
The one born in 1795 is a red herring. Annabella can also be ruled out; not only are her parents not Robert and Ann(e), but she is with her parents in Minto in 1841, 1851 and 1861.
It looks very much as if the record of your Ann(e)'s baptism, if it ever existed, has not survived.