Caveat Emptor: You are trying to do or modify something that is connected to mains voltage. Please tread very carefully and do additional research.
A few notes on your question and assumptions.
* USB is a 5V device, not a 12V device
* A lamp that was designed to handle G4 bulbs will already have a 12V transformer built in.
* If you just want to power the G4 LED bulb (in it’s accompanying socket), then you need a 12VDC, constant current power source. The current required will vary depending on the bulb so it would be best if you have the specs. If not, you can tinker a circuit in series with a multimeter and play around with different current levels. Higher current will give a brighter output but also shorten life.
* If you want to stick with USB (5V), then you can find individual, high brightness LED’s and create a drive circuit with a series resistor to modulate the required curent.