I need to travel from La Paz, to Salar De Uyuni and then to Chile, and from Chile come back to Peru.
For "safe", I mean reliable companies in terms of delays/broken engines but also with good reputation about thefts.
None is completely reliable in that part of the world. Bring plenty of patience and plan a good amount of time between bus arrivals and departures.
The La Paz - Uyuni segment is the roughest. While you can do half (Potosi-Uyuni) on train which is more comfortable, it makes logistics more complicated. Train cancellations are common and so are bus ones but at least there are a lot more buses going back-and-forth.
If you do not mind going back to La Paz, you can do a round-trip to Uyuni by plane which is what I would do having done the bus to Uyuni route 2 months ago. While I had booked a more spacious bus, a few hours before its departure I received a call saying it broke down and had to take the regular bus which transports more locals than tourists and makes more stops. This one was supposed to take 12 hours, instead of 10 for the tourist bus, but it actually tool 22 hours which include two flat tired, road-blocks, detours and taking the wrong route! It won't surprise you that I flew back after that.
Peru buses are clearly a level ahead of those in Bolivia with fewer delays and more space per person. As they are more touristy though, you get more thefts in Peru than Bolivia. Inside the bus is not much of a problem if you keep your things close but watch where your luggage is at stops. If you cannot see it from where you are seated, exit at each stop and hop back on when the luggage compartment closes.
I don't think you will have any problems with theft in the buses. They are used by either tourists or people working (and I honestly suggest you keep an eye on tourists!).
But don't expect comfortable and 100% reliable buses with air con and snacks. Buses from Peru and Chile are usually better than Bolivian ones, and around La Paz there are quite alright.
The only 'complicated' part is if you are going from La Paz to Uyuni. If you can, avoid the buses for this part. If you are not used to 'hardcore' traveling, you will have a hard time. The road goes over very high cliffs, the journey takes a very long time and most of the buses don't have a toilet (they stop at certain places that have them, and you can ask the driver to stop too if you are in the middle of nowhere). Trains are more realiable, they are comfortable, they don't usually fall off cliffs and you can pee inside them! They depart 3 or 4 times a week, and you will probably need to book in advance.
'Reliable in terms of delays and broken engines'... well, none of them are. South-american countries are in a constant struggle, it's getting increasingly better, but it's 400 years of history of exploitation. I guarantee you won't have any problems with the locals though, most of them will offer you everything they have even if it's almost nothing.
In chile at least, the most reliable (but sometimes expensive) bus company would be Pullman Bus.
Almost a month ago I had a violent accident in Bolivia. Luckily, I'm pretty good, but do not want this happen to someone else, so I'll tell you my experience.
01/04/16 Patty and I traveled to Bolivia. We had a whole plan between La Paz, Uyuni, Copacabana, Puno and Cusco. As we wanted everything to go well, reaching La Paz we bought our tickets and tours in a travel agency. We booked bus tickets La Paz-Copacabana for 01/07/16.
On 01/06/16 we were in Uyuni and we received a call from the agency to tell us that we have to change the bus company because there was a strike in El Alto. They offered us that we could store our bags, that the bus had wifi and would be a good experience. Obviously, it was all a lie. The company was TRANS INTERNATIONAL TITICACA also known as TITICACA TOURS.
01/07/16 we arrived at 6:00 am to the bus station. Everything was a mess. They sold tickets in excess, they put us in any bus, we boarded the bus like cattle and the tourists even came up with the bus almost underway.
Of course I complained but I was ignored, we were treated terribly and the spokesman answer that "if you do not want to take the bus, there are other people who will do it." Unfortunately, we hadn't enough time and we had to be at our destination because we had to take a plane to Cusco.
The bus left shortly before 7:00am. The first part was a trail, because of the strike we took an alternate route. By 8:30 am, we were on the road usually used to go to Copacabana.
About 10:30 am, apparently by mechanical failure (the brakes broke), the bus began to wobble, then accelerated, crash into a mountain and flip up. The bus was shattered and some of us flew through the windows.
Due to the severity of the accident my friend and I were hospitalized for almost a week in El Alto, Bolivia. The owner of the company appeared four days after the accident (not by choice) and he wanted us to sign some papers. It was a horrendous treatment and, in short, told us that if we wanted to sue the company we can do it; we have to say that there was no apology involved.
Please, share this post. No one is free from an accident and also often of totally unpredictable events, but in our case was more neglect than anything else. I don't want that this happen again. No one should go through what we had!!
If you know anyone that is traveling to Bolivia, tell them to never ever take TRANS INTERNATIONAL TITICACA (TITICACA TOURS). They do not care about people life.
Investigations are under way in Bolivia. The company still continue operating in Bolivia and Perú. Help us to prevent this from happening to someone else.