While located only 20 miles from La Paz, there is no direct public transporation from La Paz to Chacaltaya. If you don't want to pay for a tour, taking a taxi may be a better option.
A taxi from La Paz (after negotiation) would be about Bs. 200 ($28 USD). To make the trip less expensive, you could first hop a Micro from La Paz to El Alto. Green Micros run from central La Paz to Plaza Ballivian in El Alto, and cost only 1 Bs (about 15 cents US). From there, a taxi to Chacaltaya costs about Bs. 100 ($15 USD) after negotiating. You'd want to make sure that your taxi will wait 2-3 hours for you, for the return trip.
There are two official taxi types, regular which are all over the city and radio which are dispatched to pick you up and take you directly to your destination.
Depending on your Spanish language and negotiation skills, you might want to engage a radio taxi for the trek to the mountain.
Bolivian Life, written by expats Brig and Dan, suggest the Easy Taxi free app to solve taxi problems for tourists.
All you have to do is register your location on the map and click “Call Taxi”. You are then sent the driver’s name, plate number, phone number and a photo so you have several ways of verifying the person driving the taxi. You can also locate your drivers whereabouts via a map which is updated in real time. It’s a wonderful resource for travelers looking for safe and reliable transport.