IAD-BOS fares (and reverse -- they are symmetrical domestically) start at $74 in BE and $104 in main one-way when connecting via EWR. As others have noted, with any connection over 4 hours domestically (US48) you will have to "break" fare and purchase separate fares on IAD-EWR and EWR-BOS legs. EWR-BOS fares start at $49 in BE and $79 in main. However, IAD-EWR non-stop, one-way fares start at $219 in main (there are no BE fares on this route when booking as one-way non-stop). Fare combination restrictions prevent combining BE fares with Main on one ticket, so cheapest ticket with IAD-EWR + EWR-BOS fares (with layover over 4 hours) would be $298 one-way.

Note that there are also roundtrip fares on IAD-EWR (with minimum stay requirements) which start at $148 roundtrip in BE and $208 in main ($74 and $104 each-way).