The easiest option to get to this reserve is to buy a tour.
The cost of an excursion to Ein Gedi, depending on the company, time of year and place of departure, can vary from 50 to 80 US dollars per person.
Just be careful: in Ein Gedi there is not only a nature reserve, but also a spa complex on the shores of the Dead Sea, where you can also take excursions. Therefore, before purchasing a tour, be sure to check with the company whether a visit to the reserve is included in the program.
You can also get to Ein Gedi by public transport. Once a day, bus number 421 departs from the Arlozorov bus station in Tel Aviv (this is not the central bus station, but the one located in the north of the city, near the central railway station). Departure time for Ein Gedi is around 8.40 am. The return bus leaves from Ein Gedi at 14:27. The drive to Tel Aviv will take about 2 and a half hours.
Considering that the cost of a one-way bus ticket is about 45 shekels, you won’t be able to save much on such a trip. And there are much more risks compared to an excursion. If you miss the return bus, you will have to get to civilization with several transfers, which will take much longer.
Please note that Ein Gedi is an oasis located right in the desert; transport there is very rare.