The Bene Gesserit were, first and foremost, manipulators.
They saw themselves as protectors and guardians of the racial destiny of humans, rather than rulers.
The distinction between "hard power" and "soft power" is largely semantic, in my opinion. Power is power, and the specific mechanisms of the power are secondary to the outcome of exerting that power.
I don't believe there was any indication of Bene Gesserit armies. Indeed, the intensity and level of training that the Bene Gesserit initiates underwent would make it difficult to field large enough numbers to maintain a coherent army, while simultaneously maintaining their existing network on field agents (ranging from concubines and wives involved in the breeding program to House Truthsayers, mediators, diplomats, and agents of the Missionaria Protectiva).
While I have little doubt that the Bene Gesserit could raise an army, given suitable motivation, the normal training initiates receive lend themselves much more to elite commando squads (and indeed the prequels and sequels published by Brian Herbert make explicit mention of such Bene Gesserit squads and training). This is in keeping with the general theme of more subtle action by the Bene Gesserit organization; even their more direct interventions are generally as discreet and covert as possible.
As far as economic power, they were a silent partner of CHOAM (along with the Bene Tleilax), so it is highly probable that they had a significant presence in the economy of the Imperium, and were likely to be able to exert considerable economic influence should the need arise. Generally, however, it seems they prefered to stay within the theme of manipulation and indirect influence, using their resources more often for bribery than overt pressure.
The defeat of the Bene Gesserit by the Fremen really wouldn't be that puzzling. The Fremen (and even the Imperial Sardaukar) were not far behind the Bene Gesserit in terms of hand-to-hand combat abilities. However, by the time the Jihad had reached the point where Bene Gesserit would be part of the conflict, the Fremen had become veterans of coordinated mass combat. The Bene Gesserit, however, were still scattered, and those who were combat trained (arguably all of them, although it seems likely that only some of them received more than basic combat training, as the levels of abilities varied; e.g. not all sisters were trained as Truthsayers) were not trained for coordinated combat. Rather, the combat training was as individual fighters or as semi-autonomous members of small squads.
Even the best trained commandos will fall against superior numbers.
However, I don't recall the Fremen actually explicitly fighting the Bene Gesserit during the Jihad. While the fighting raged on every planet (except for Caladan), I don't believe the Bene Gesserit were explicitly targeted, nor do I recall mention of an active resistance by them.
Instead, the Bene Gesserit are still relatively intact after Muad'Dib's Jihad, although their power gradually dwindles up until The Scattering, at which time they re-emerge as one of the major powers competing for the power vacuum left by Leto II's demise.