Lethbridge has only 75,000 population, but is spread over a large area. Public transportation exists, but provides a slothfully slow method of getting across the city. A ten minute trip by auto can take 90 minutes by public bus. Few people ride the bus because of its poor service and the city provides little service because few people use it.
The best way to get around the city and surrounding areas is by car or motor cycle. This way you can get out into the rural areas. In spring and early summer, the immense irrigation projects create a huge mosaic of colour. An intense yellow field of canola beside a field of blue flax in the right light will blaze a photo in your mind for life. You need to take time to tune into the quiet immensity of the country to truly appreciate it.
From Calgary: drive south on McLeod Trail. When you pass under Highway 22X you are on Highway 2. Follow Highway 2 to Fort McLeod, 150 km south. Follow signs to Highway 3 East. Follow Highway 3 abut 100 km and you'll be in Lethbridge.
From Montana, USA: Follow Interstate 15 north to the border at Sweetgrass, MT/Coutts, AB. From Coutts, follow Highway 4 north about 70 km to Lethbridge.
Lethbridge has a bus system. I've never ridden it. Since you've likely driven there, you probably have a car. Use it. The main streets are: Highway 3 (Crowsnest Trail) which cuts right through the city parallel to the CPR Line. Whoop-up Drive connects downtown Lethbridge to the university and the historical site at Fort Whoop-up. Mayor McGrath Drive runs south from Highway 3 at the east end of town toward Highway 4 and the US broder.
There are 2 charter buses that will take you to/from Calgary from/to Lethbridge: Greyhound and Red Arrow.
The bus will take from 2hrs and a half to 3 hrs, depending on traffic. There are several departures daily and prices vary between 40-60$. Double for a roundtrip.
Schedules and rates can be found here: http://www.busbud.com/en/bus-schedules/Calgary,Canada/Lethbridge,Canada