National Express coaches leave from outside Luton Airport's main terminal and it takes 9-12 hours to travel to Edinburgh, including a transfer in Milton Keynes. The first bus leaves at 08:25 with one later morning and two overnight buses. A single ticket costs 53 GBP or from 70 GBP for a return between Luton Airport and Edinburgh.
If you book more than seven days in advance you will also get a cheaper fare. After booking online, you will be issued with an e-ticket, which you need to print out and take with you, or an m-ticket, which is sent to your mobile phone. Otherwise you can get at ticket at the station.
If you cant find a cheap ticket to Edinburgh try looking for Glasgow which is only 30 minutes away from Edinburgh. From Glasgow you can get to Edinburgh by local bus service or by train so this could work out better value.
By train the best route is from Luton Airport to Central London then to Edinburgh. There are around three trains per hour from Luton Airport Parkway to St Pancras Station in London. On arrival at St Pancras, transfer to the adjacent King’s Cross mainline station (follow the signs) to catch your onward connection. The total journey takes 5 ½ - 6 hours. The journey costs around 60 GBP single or 186 GBP off peak return.
The UK train ticketing system is notoriously complicated. It is usually cheaper to buy your tickets up to 6pm on the day before you travel than on the day. And fares are more expensive if you travel before 09:30. You get the best fares by booking up to three months in advance. You can buy your tickets online, at the station ticket counter, or from the ticket machines on the main concourse. If you book online you will need to collect your tickets from the ticket machine using the same credit card you used to book your tickets online.
If you have a very early flight from Heathrow Airport or arriving late you may wish to spend the night at a hotel near Luton Airport which can work out cheaper than Edinburgh.
To see other hotels in and around Heathrow airport click the following link - Luton Hotel Deals.