Tubman escaped in 1849 (twice, she made a trip back the same year to help relatives. In all she helped some 70 slaves escape.
The story about Tubman singing "I'm Boun' for de Promised Land" comes from Stedman's biography, 1869. Historians have pointed out fictions in that narrative; there is no other source that can verify if Tubman sang, or even knew, the song at that time.

Records of the song as a spiritual:
McIlhenny, Befo' de War Spirituals, "Boun' fer Canaan Land." Not seen. Date of collection?
H. E. Dann, Fifty-eight Spirituals for Choral Use." Not seen. Date of collection?

The hymn was originally written, lyrics only, by Samuel Stennett, 1787. It was revised and included in the Sacred Harp c. 1844.
I will post the one from the Blaylock Collection shortly.
There are several spirituals-gospel songs based on these, also use of lines float from one song to another.