A $350K bond is quite large. A bond of this size will take more than good credit to qualify for. You will need to have substantial assets to back it up. Your best bet is to apply to see if you can even obtain a bond of this size at:
JW Surety Bonds - Commercial Bond Applications
It sounds to me like they are purposely limiting the amount of new contractors getting licensed. If not on purpose, then someone did not do their homework when creating these requirements.