Is the song You - Ten Sharp in B Dorian scale?

Possibly so.


Right hand plays firstly the B minor chord. Then E major instead of E minor ie G is sharp.


By the way on all the first 3 chords, the bass is pedal bass, ie constantly at B.


3rd chord is G major with B bass.


So overall the harmony code is;


(The notes F, G, C are sharp since scale is B Dorian)


B         ie B D F
B(4,6) ie B E G
B6       ie B D G(natural)


Further reading:


Bach Bass Rules:


https://normanschmidt.net/scores/bachjs-general_bass_rules.pdf