You can't just cut off the bottom piece, you are correct in that it converts voltage.
The bike is 12v and the Garmin is something else (probably 5v).
You could get a female cig lighter socket and wire that into your bike, then plug the garmin into that.
Or, you could take the bottom piece, isolate the circuit board and solder in leads in place of the cig lighter tip and tension bits (not sure what they're called?).
Or, you could see if Garmin (or aftermarket) sells a direct-to-battery harness (with the transformer) built in like they do for the Zumo's. We did that for my dad's non-Nuvi, non-Zumo garmin, with one of these:
3A 1Meter DC 12V 24V to 5V Rigth Angled 90 Degree Mini USB Power Converter Cable | eBay
(although I don't know if your Nuvi uses mini-USB and whether the plug angles the right direction for your purpose)
The bike is 12v and the Garmin is something else (probably 5v).
You could get a female cig lighter socket and wire that into your bike, then plug the garmin into that.
Or, you could take the bottom piece, isolate the circuit board and solder in leads in place of the cig lighter tip and tension bits (not sure what they're called?).
Or, you could see if Garmin (or aftermarket) sells a direct-to-battery harness (with the transformer) built in like they do for the Zumo's. We did that for my dad's non-Nuvi, non-Zumo garmin, with one of these:
3A 1Meter DC 12V 24V to 5V Rigth Angled 90 Degree Mini USB Power Converter Cable | eBay
(although I don't know if your Nuvi uses mini-USB and whether the plug angles the right direction for your purpose)