Let me just try to clarify a little bit here.
We all know how ambient lights work and how bump maps work... right?
So... when you say, 'how can I get a bump map to work with just ambient lights,' what exactly is the effect you're going for?!
If your scene only has ambient lights, then an object--let's say a sphere--must appear to be a flat-colour circle when rendered, because every point on its surface receives an identical amount of light.
Now let's say you've got a bump-map of bright 'bulges' on a dark background.
In a normal scene lit from above (let's say), the bits of the sphere's surface that were on the top part of each bulge would be brighter than before... the bits of surface on the bottom of each bulge would be darker. If you made the light come from below instead of above, this would be reversed. Right? Simple. Fine.
But... in your ambient-only scene... exactly WHAT parts of the map do you want shaded brighter, or darker, or whatever? How will Maya know which parts should be lighter or darker?! With reference to what? The world up? The direction of the camera? The direction of some phantom directional light that isn't actually casting?
As several people have pointed out, saying that you want 'bump maps to work with ambient lights' is, phrased just like that, meaningless (because the concepts are incompatible). You say you understand this. So... you need to be more specific about what you want to achieve.
In this case I think a few screenshots would be worth a thousand words. How about one shot of some test object with your ambient-lighting-only setup and no bumpmap; one shot with the bumpmap and a regular light to show the look you're going for; and one shot of it with that same bumpmap and your current ambient-only workaround?
Good luck!
-Steve