The Great Mouse Challenge

Yesterday, I was sitting at the table by the patio door making journals.  Something caught my eye and looking out I was quite shocked to see a tiny little mouse being as bold as brass carrying a piece of straw from the rabbots hutch.  it carried it to the edge of the path and then disappeared underneath.  I watched to see the mouse emerge again and this time it went scurrying over to the slope of the hutch (allows the rabbits in and out of their cage all the time)the mouse then managed to get into the hutch, manouver the internal slope, grab some food and retrace it's steps.
Now if the mouse was in my house, I would probably not be as calm, but this one is firmly outside.  I went and looked up what type of mouse it was and found out that it was a field mouse.  apparently their breading period is March to October, so I have a few weeks to get rid.  I am certain there is only one, but he / she is definatley here for the long run as it's built a nest down a tunnel and is emerging and carrying straw down there.

I have a humane trap.  It allows the mouse to go in and then closes a door behind it.  It can catch more than one mouse at a time.  You then have to trust that the trap won't allow the mousie back out and you have to take it two miles away from your home and let the little chap(s) out.  I am pretty certain that there is only one.
Yesterday I enjoyed watching mousie running around, but although the trap was baited with peanut butter (supposed to be the best attracter) the mouse climbed on top, ran around it, but failed to venture inside it.

This might be a trickier challenge than I thought.  I don't want to use a conventional nasty back breaker, but how am a going to catch it.