USB provides a maximum of 500mA. Although there are requirements for devices, not all PC's adhere to these, and some are overly strict in what power a device can draw. I have seen USB provide 600mA, but some will kick up a fuss if you draw more than a few on standby (no device connected, just drawing power). Devices for low power, often tell the USB host they require 100mA max, so the host monitors this. Drawing more current than a device tells the host it needs often results in a blue screen.
All that said, with no device attached and literally just connecting to the USB powerlines, for the most part, you could draw 500mA without much trouble. I jstu thought I would warn you in case you got a blue screen
for minimum USB voltage of 4.25, with the minimum max current draw of 460mA thats 1.955Watts. Your requirement of 6V @ 350mA is 2.1W. Could be tricky. Even if the USB port provided 500mA exactly, thats still only 2.125 - 2.625W. This doesn't leave much margin for error, and requires quite an efficient boost converter.
What device are you trying to power? It may very well happily operate at 5V, or its 350mA rated current draw is an absolute maximum (they usually give the maximum requirement for headroom). And if it can be powered from batteries (for 6v, thats 4x AA's) then I'm sure it can operate at a slightly lower voltage, since a battery's voltage drops slightly as it discharges. Although, at 5V, that would mean each battery is at 1.25V, which many devices consider to be 'pretty dead'.
I am hesitant to recommend the venerable MC34063 chip, because its efficiency will be somewhat disappointing when compared to IC's specifically for this task. Thankfully your current requirement isn't sky high, with a continuous input current of 0.5A, I ithnk we can safely say the peak current will be around 1A. May I ask what parts/distributors you have available to you? Although it takes all the fun out of it, sometimes a simple 'module', whilst being more expensive, can save you time and hassle.
Blueteeth