I do not think it is a good alternative.
Check different trains schedules for better pricing
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Yes, you can take a bus from Cusco to Santa Maria, then a minibus to Santa Teresa and then a minibus or shared taxi to Hidroelectrica. Then you walk to Aguas Calientes (2.5 hours, nice trail, quite scenic). Easier (and that is what we did) is to take a shuttle from Cusco or Ollantaytambo straight to Hidroelectrica. That was 80 soles return and about the same price as going by bus. Yes, you would have to pay for lodging in Aguas Calientes (we had a double room for 60 soles). So still quite a bit cheaper than the train. And you might want to sleep in Aguas Calientes anyway even if you take the train. It depends on whether you buy a morning ticket for MP (which you have to do if you want to hike up one of the mountains) or an afternoon ticket. The next morning you would take the bus to the MP entrance ($12) but you have to do that if you go by train as well. You can also walk up to the entrance if you want to save money. The bus back to AC is another $12 or walk down (easier than walking up). It would be best to have 3 days so you don't have to rush your day at MP.
We went by shuttle from Ollantaytambo to Hidroelectrica, walked to Aguas Calientes, stayed overnight in AC, walked up to the MP entrance in the morning, visited MP, hiked up MP Montana, walked back to AC, had a relaxed morning in AC the next day, walked back to Hidroelectrica and took the shuttle back. We did that in January but we were lucky because it hardly rained that January. That road can be dangerous (or even impassable) in the rainy season. I don't know when you are going.
M>P> is the most over priced tourist site on earth if you take the train.
Many travelers are skipping it these days because of this .
For people who are fit, like to hike and have, ideally, 3 days it is possible to get to MP for 80 soles: shuttle (80 soles return) to Hidroelectrica, scenic walk to Aguas Calientes, walk to MP entrance, visit MP, walk back down to AC, walk back to Hidroelectrica, shuttle back to Ollantaytambo or Cusco. Add to that the MP ticket and going to MP costs $85. And that is if you hike up a mountain at MP. If you don't it is less. Our hotel in AC was $18.
world sites we visit
Giza pyramids Cairo =10 us dollars
Taj Mahal India =20 us dollars
Angkor Wat- Cambodia 20 us dollars
Valley of the kings Luxor Egypt=10 us dollars
coliseum Rome =20 us dollars
M P + 152 us dollars and another 175 in cost to get there Rip off totally