IIRC you’re on console, same as I am. It’s a bit wonky on console. I remember being very confused.
I’ve reloaded my old save, and this seems to work:
1) have Great Banker selected.
2) with left-Thumbstick drag a line as if you were trying to move him, drag the line (showing hex-by-hex and turn-by-turn indication of movement) all the way to enemy capital — I think anything in the capital’s radius works. Don’t click on the A (Xbox) / X (PS) button, that’s what you normally click on to move a regular unit.
3) with that line still there, use the d-pad to move between the “Move”, “Skip-Turn”, “Travel-to-City”, and “Activate-Great-Person” buttons, in the bottom-right (same ones you use to skip turn or fortify for Military Units). D-pad over and select the Travel-to-City button and now press the A (Xbox) / X (PS) button.
4) you should instantly move to that city. It only seems to work with enemy capitals, not other cities. I just tried it out and you can move to partly uncovered capitals even if you haven’t actually seen the city center yet (just zapped to Hatshepsut’s capital which I could see the corner of the Eiffel Tower peaking out behind the fog of war).
5) Wait a turn then with the Great Banker selected, d-pad over to the Activate Great person.