Any advice on easiest, most economical way to get from Liverpool to Inverness, hopefully in one day, by train or bus. Don't want to drive or fly. Thanks.

Checking further - Single bus journey is £58. Train single varies from £43 to £94 depending upon how far in advance you book. Train is quicker. If going via train then in Glasgow you have to walk 10 minutes between stations.

Coach is certainly simpler. One change in Manchester, 11 hours and a fare of £58.
National Rail Enquiries site has £94 for a standard single ticket, and roughly an 8 hour journey with 2 or 3 changes.
Journey 4 here http://ojp.nationalrail.co.uk/en/pj/fa has FIVE changes. Bet that´s fun.!

#3 'fraid your link has expired so can't tell what you actually found.
However a similar journey I have found is actually only 2 changes if you go into details - at Warrington and Glasgow. The other '3' are because you have to change stations in both towns and changing to and from a walk counts as a change.
The cheapest possible fare is £13.50 by train though how often tickets are available at this rate I've no idea. £34.50 is easily achievable with advance booking

The web site is http://www.nationalrail.co.uk.
Damn it, I can only get down to £40 on this site where are these £34.50 and £13.50 fares ?
My £40 trip was only one change - at York !
Edited by: pedro555

Note that return train fares are normally more expensive than two singles. Bus returns are only slightly more expensive than one single.

The bus will be an absolute nightmare, traffic between Glasgow and Stirling/Perth is often terrible in and around rush hour and Perth-Inverness is an awful road and takes ages.
Train is the way forward. Liverpool - Wigan, Wigan - Glasgow, Glasgow - Inverness.
In Glasgow you will have to change from Glasgow Central to Glasgow Queen Street but the walk is less than 5 minutes and very straightforward (right out the station, left on Buchanan Street, you'll see Queen St Station on your right). If you have bags and cant be bothered with the short walk there is even a free shuttle bus between the stations that picks up/drops off right outside the main entrances to both.

#6 Note that return train fares are normally more expensive than two singles
Things may be different now of course, but from my days traveling extensively on UK trains, that was never the case.
Sometimes a return ticket was only a pound more than the single fare.
As I say, may be different now.