It's hard to say exactly, because normally I would bike everywhere anyway (never had to have a car or drive in all my 41 years; though I could, there's no reason to, and I'd rather not).
However, there used to be times I'd rather take the bus, or more recently the light rail, for across-valley trips, especially if cargo (like bigger items from Freecycle) is involved. So on those trips, I've saved at least a couple hundred dollars on the bus fares in the last couple years, where before I would have taken the bike on the bus just because of the summer heat, for most of the trip. Although, in some cases, because of the cargo or length of trip, I've taken the bike *on* the light rail or bus.
No savings there.
Since the recharging only costs a few cents at most, I doubt I've even spent enough for a single all-day fare pass yet.
Now, as to how much the bike itself has saved me, ebike or not, well, I'd've probably gone the car route like most do if I didn't ride the bike, and that'd be the cost of car payments, insurance, maintenance, registration, testing, etc. Probably at least several hundred dollars per year, *before* fuel costs, and potentially a few thousand a year, depending on the car and the insurance.
Since the bikes themselves don't usually cost me anything, coming to me as scrap, and the same for all the used batteries and motors and stuff, it's pretty definitely a huge savings. I think over my whole life I might've spent $100 on bikes and parts for them. Maybe another $50-$75 on tools that I still have and use (except for one really crappy chaintool that disintegrated, so there's $10 wasted).
Overall, I'm sure I'm saving a significant amount; I just haven't got an easy way of determining how much.