Buses and taxis are quite frequent in Lesotho, even in the farthest reaches of the country. I was amazed at where the taxis went - on roads where I thought only four wheel drives could go. There is also a Biz bus that does the rounds, some folks staying at Malealea took it while we were there. There are even four wheel taxis that take the notorious route via Sani Pass between South Africa and Lesotho, which would make for an extremely bumpy ride I would imagine.
If you're driving around, get a topographic map of Lesotho. Though the 'latest' edition is ten years old, it is well worth the investment. Many hotels and lodges stock them, most definitely Malealea Lodge. With it you'll be able to track your progress quite accurately and anticipate certain things like river crossings and steep inclines. It'll also help you discover out of the way roads that may not be indicated on ordinary road maps.