Chuffin ‘eck. Supposedly the cheapest place in town wanted £25/week! that sounds roughly the right ball park for somewhere that is actually secure with reasonable access time and short term rentals etc. That won’t include insurance (you’d need to check if your house insurance would cover it off site like this). Never been that convinced about security at some of these places, minimum wage guy on the gate etc.
Your “feeling of violation” will still be there if the break in when you are away and rummage around before realizing the bikes are not there.
If you can’t trust the housesitter to lock up afterwards then don’t use them. It its just the “theoretical risk” then the same applies every time that you / your wife (etc) leave the house.
Its also quite likely that you could go away for 2-3 weeks leaving the house completely unlocked and come back and everything would be exactly where you left it!