The best and the cheapest way to get from Ashdod to Masada are not necessarily the same.
Cheapest would be to take a bus from the Ashdod bus station to Jerusalem and then another bus from Jerusalem to Masada. For schedules and other information check www.egged.co.il/eng
Best would be by car - either a rental or a taxi that would drive you there directly, and be able to return you just as easily. This would also be fastest - each direction about 2 1/2 hours - by bus figure one way about 4 hours.
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