If you've got a gap where air is blowing in, then you might be just as well putting some 'expanding foam' into the gap to block it up.

Yes, you could put insulation under the bath - the wires don't carry current, they are there to act as an earth safety in the event of a short, to make sure that you don't get electrocuted. If there was a short then it should trip out in the fusebox, so you wouldn't have live current running under there for long enough to ignite anything.

Fibreglass would probably be best if you were concerned about fire - it's hard to ignite.

You can simply lay some old carpet or vinyl floor covering neatly over the floorboards. Insulation, especially fibreglass will allow airflow through. Another cheap option is EPS. This is the white polystyrene that you can buy anywhere in sheet form. Closed cell is the best, Cellotex or Kingspan, as it is moisture resistant and being in a bathroom it will get very humid. Bear in mind that insulation is not effective when wet, so if it gets wet or damp it is not performing. Personally I would just use floor covering to stop the draughts. Cheers Concrete