The exact answer to this question is that we are not told. I have carefully checked the poem again for any time references that could give us an indication, but no specific time markers are given to us. The only thing that we can deduce is that the Mariner has been under the curse for a long time. Note how he is described in the penultimate stanza of the poem:

The Mariner, whose eye is bright,

Whose beard with age is hoar,

Is gone...

We can assume that the Mariner would have been a young man when he had this experience, and his aged state as described in this stanza suggests therefore that he has been wandering and sharing his tale with the supernatural compulsion that he describes for a long time. Killing albatrosses has its consequences, obviously. ...