Using a 9 speed cassette with a 11 speed shifter I've just bought a turbo trainer and I'm looking to buy a new cassette/wheel/tyre to use to save the ones currently on the bike and make it easier to change between my bike and my girlfriend's bike too (easier than changing the tyre all the time).

I have a 105, 11 speed set up - will this work with a 9 speed cassette on the turbo trainer wheel?

thanks
Nope.

Above 6 (or 7, can't remember which) speeds the spacing of the sprockets gets narrower as the number of sprockets increases. So, you can't use a cassette with a mismatched number of sprockets - at least not for the full range of the cassette. A 10 speed cassette would work slightly better.

If you want to minimise cost of the extra wheel, find the cheapest used 10 speed rear wheel you can and an 11 speed cassette that will fit on a 10 speed freehub body.