There are presently no regular routes that will drop you near the entrance to the park, that said you will have to come with a charter or remis from Valle Fertil or La Rioja.
there are charter buses that leave the bus station in San Juan city. (Vallecito company)
From San Juan City:
Route 20 for about 60 km to Natl Rt 510, will get you to Valle Fertil- 260 km total.
from Valle Fertil- continue on Rt 510 then Natl Rt. 150, this will get you to the park- 80 km (60 of which is under construction being paved...check date)
I went with a local guide who picked me up at the airport in San Juan, we went all over the province and dropped me off at the airport at the end of my trip. Easier that way:)
There are only two buses that leave San Juan's main bus terminal to Valle Fertil. Your best bet is to take the early bus at 7:30 am so you can get into town during day light to secure accomodation. The bus ride takes four hours unless your bus is fortunate enough to break down and then it will take a whole lot more.
There is another bus that leaves San Juan at 1:30 and arrives in Valle Fertile around 5:30.
When leaving Valle Fertile get your ticket the night before. The bus leaves to San Juan at 3:30 am and then again 1:30 pm. This really stinks if you are trying to get to Mendoza. You really should try to take the early one and not get stuck in San Juan.
It is possible to go from Valle Fertile and Pagancillo and visa versa but you must organize through an excursion to Ischigualasto and Talampaya. The Rangers at both parks are pretty nice about giving rides back into town after the park closes.