Flybe operate an Inverness-Southampton service. Unfortunately it doesn't go on a Saturday but you could always fly down on the 24th and stay overnight. The baggage allowance is 20 Kgs plus a 10 Kg hand baggage allowance. You can take extra kilos and indeed extra bags but the price shoots up. The price for the one way trip is £60 per person as of today (20/01/09) including one hold bag. Don't know about the price of the return flight as I don't know what day that would be. There are a choice of hotels in Southampton ranging from Premier Inns to the 5* De Vere Grand Harbour (not worth the money IMHO).
We did this cruise in June and we flew from Aberdeen to London Heathrow where we were met by coach and taken to the ship. Our flight from Aberdeen was at 6.15am and we were on the ship by 11.30am.It is a long way from Inverness/Aberdeen to Southampton so flying would probably be your best option.
Bear in mind that if you fly to Southampton you will be restricted by the airlines baggage allowance (Probably 20 kilos). When I went to Southampton last year from central Perthshire I drove and stopped at a Holiday Inn Express in Droitwich (£45 for the room). This drive took about 7 hours and that included some shopping at Gretna Outlet stores ! This gave us time for a nice calm drive into Southampton where we parked the car at the terminal and within 20 minutes we were in our cabin on the QE2. No baggage restrictions...no hassle and a cost of approx £170 (including hotel on the way home).
Another option to investigate is, some of your local T/A's may have special travel arrangements, deals etc. in view of the distance involved.
Which coach company does transfers from Preston to Southampton to link with Royal Caribbean IOTS.