National Express coaches leave from Parkside in Cambridge. There are two buses a day that take 10-12 hours. The first coach leaves at 08:40 and the last departs at 09:20. There is an overnight service that departs at 20:20. You need to change once, either in Milton Keynes, Birmingham or London for your final destination of Elder Street Bus station in Edinburgh. A single ticket costs 59.60 GBP or you can get a return for between 56 GBP - 79 GBP.
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 bus station.
If you have more time than money or fancy stopping off in London before making your way to Edinburgh you may be interested in looking at Megabus who operate value bus services to Edinburgh. Fares can be as little as 5 GBP for a single if you book far enough in advance.
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.
Trains run approximately hourly from Cambridge Station, and the journey time to Edinburgh is between about 5 ½ hours. You need to change trains in Ely and Peterborough (some trains go direct to Peterborough, where you can take your onward connection). A single ticket is 86.50 GBP or an off peak return is 108.30 GBP.
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.
Travel by plane is the fastest, and probably the cheapest way to travel between Cambridge and Edinburgh. The train is the most eco-friendly option, and doesn't take much longer than flying once you've factored in the travel between the airports and the city centres.
Easyjet flies from London Stansted to Edinburgh up to five times a day, and the flight takes one hour 15 minutes. Depending on how far ahead you book, a single ticket costs around 21 GBP - 65 GBP. Be careful, there are a number of extra charges that can give you a nasty surprise. It costs 6 GBP to check one 20kg bag into the hold. A 5 GBP charge for travel insurance is automatically added unless you remove that option when you book online. The website also suggests you buy a Speedy Boarding pass for 5.50 GBP, but this is unnecessary.
To get to Stansted Airport you can catch a train from Cambridge, which takes 30 minutes or 60 minutes and costs 9 GBP one-way. There is also a National Express coach that takes 50 minutes and costs 12 GBP for a single ticket. You can buy your ticket on the coach, which departs from Parkside 21 times a day (check the times before you travel, as there is sometimes more than an hour between buses). Check in at least 40 minutes before departure, and show your passport, otherwise you will be denied boarding. Easyjet sell a limited selection of sandwiches and refreshments onboard, but you might prefer to take your own.