I wouldnt and I'm pretty sure your local town code wouldnt let it pass either. I'm not and engineer, but it seems the srength of the ledger is the multitude of bolts holding it across its total length. FYI, most codes don't allow ledgers to be attached to cantilevers, which is what your bay window is if I'm reading it correctly. I just built a raised deck with two cantilevers; one a bay window and the other a fireplace. We had to run the joist wild under the cantilever and attach it to the house underneath. This made the floor lower and may require an extra step to the door, but the building dept would not allow it any other way.

I'm not an engineer either, but I disagree with Peak. I don't see why 3 sections of ledger board would be any weaker than a single one, as long as they're all sufficiently bolted into the rim joist. If you think about what's putting load on the ledger, it's the joists that are butted into it and the boards on top of them. A long ledger is supporting all the joists collectively, but a short ledger only has 3 (or 5 or whatever) joists bearing on it.

You are correct that the ledger needs to be attached to the main rim joist, not a cantilevered bay. But it sounds like the OP's bay may be built in such a way as to support the ledger.

Got pics?

I agree with weedy and have seen ledger boards pieced in the past. As long as it is thru bolted to the rim joist should be no issues.