KevinM As pianolverus says, this is not by Bach but copied into the Anna Magdalena Book. The original is in E flat.
It was from an opera by August Stoelzel, which is lost apart from a couple of arias, of which this is one.
The transcription usually known here (the UK) was made by William H Harris, who was choirmaster at St George's Windsor and had Princesses Elizabeth (later ofc the Queen) and Margaret in his choir during WW2. The transcription was made for Maria Donska, who was a Polish pianist taking refuge from the Nazis in England. She subsequently made her career in the UK.
The Anna Magdalena Book itself has a noteworthy history. originally, Bach intended his French Suites to be his wedding present to her, but because he was obsessed with augmenting and changing his compositions, by the time wedding day came round, he had scribbled on it too much for it to be tidy enough to give as a present. So, in the 'great composer' equivalent of buying flowers from the garage on the way home on Christmas Eve, Bach cobbled together the Anna Magdalena Notebook, largely other people's elementary works, and including blank pages into which Anna MAgdalena later copied stuff herself.
wikipedia and many other places have the full words of the aria, but of course the epigraph in the copy you have posted (that it was written by Bach to express his love) is not right.
This is mine of the Harris transcription:
