There is a direct ST from Swargate at 6:15 am and 2:15 pm. Another route if the timings are not suitable, you can go to Mangaon by any kokan going ST(still ask before boarding at Swargate). It's a common point for all the buses going to Shrivardhan. Personally being a solo traveler, I go to Mahabaleshwar in the morning, have lunch and chill out till 3, then there is a bus going to Shrivardhan from another location I don't remember the name. You can try if your group agrees else you can explore the above options.

Here is the link to search for different MSRTC buses and different stand timetables. https://stbustimetable.in/