You probably will not need to use the buses if you stay in central Leicester. It is not a huge city and exploring the centre on foot is easy and safe.
But you might want to visit some of the villages and sights nearby, such as%L[http://members.virtualtourist.com/m/p/m/db16a/Bradgate Park (childhood home of Lady Jane Grey) or the National Space Centre.
This site will give you links to all Leicester bus services and timetables, with maps showing bus stops and routes:
and the site linked below will provide you will all bus timetables for the city and local area.
East Midlands Airport (East Mids for short) is the nearest international airport to Leicester. There is a direct airport bus service from the city, although no railway connection exists. The airport website will give you details.
The airport serves budget and mainstream airlines from numerous destinations, so it's a good choice if you want to visit the East Midlands area.
You can hire cars from the airport, as is usual in the UK. There is always plenty of parking with several sites on-airport (regular free bus shuttles to the terminal) and a nearby off-airport site. It's best to book parking online in advance for best prices. UK on-airport parking is never cheap.
East Mids airport is very small, with just one terminal. There are places to eat, drink and shop, although most of these are after security. There's only one cafe in the departures area.
The big advantage of using such a small airport is that there are rarely long queues for security (other than at certain times in the UK school holidays) or for border control and baggage reclaim.
Here we are summer 98, ready to come back to Spain after a hard year lol, in my case only for a month and back again snif snif
National Express at Gravel Street