I usually travel by train and use the sleeper, brilliant way of travelling and see some of the scenery at the same time (only in summer though, winter it's dark)
Train leaves Euston station several times a day, see http://www.scotrail.co.uk/caledoniansleeper/index.html for more info.
Flybe flies from Gatwick to Inverness, Easyjet from London to Inverness.
Hope this helps, enjoy your stay in Inverness! about 5 years ago