I wanted to travel to Scotland this summer with my girlfriend, but I must admit I feel a little overwhelmed with options. Is there any carpooling service? When traveling with buses, do I have to book a ticket before or can I buy it when entering a bus?
The Visit Scotland webpage on coaches carries plenty of information on the topic, including:
Most of the inter-city and longer-distance coach services around Scotland are provided by Scottish Citylink, Stagecoach, Megabus and National Express offering most of the inter-city and longer-distance coach services around Scotland, including a connecting service between the country’s two biggest cities, Edinburgh and Glasgow.
Tickets for these services can be bought in advance by phone, online, in stations and often on board.
For busy routes and travel at peak times, such as weekends or national holidays, it's a good idea to book as early as possible to guarantee a seat.
It's worthy to note that there exist various discount cards for coaches, namely the Explorer Pass from City Link and the Megarider tickets from Stagecoach. Quoting from the aforementioned Visit Scotland page:
Discount fare options
If you plan to do a lot of travelling by coach, it may be worth buying an Explorer Pass, which offers unlimited travel on Scottish Citylink network or the megarider tickets offered by Stagecoach, which provide unlimited travel within certain areas.
Car sharing is obviously an option too. Blablacar for example operates in the UK. You might want to check it out.
Train tickets are generally expensive in the UK, unless you have a discount card. I don't know of your age group qualifies for one, but Youth Railway Cards allow for many interesting discounts. Shouldn't you fit the age group, despair not. As starplusplus usefully mentions, the Two Together railway card allows discounted fares for two people traveling together. Seems to fit your case perfectly. Ticket prices may vary a lot depending on the departure time. For some lines, there are multiple train companies offering various times and prices.