First, and most important, the ADIZ extends beyond the B-space in several areas. Do not for a second think that staying out of the B-space keeps you out of the ADIZ.
Second, it's not hard at all to go through the ADIZ under VFR, but it is very hard to be permitted VFR through the B-space from one side to the other. Potomac is very good about letting you enter the B-space to land at an airport inside the B-space, but that's about it. If you want to transit the B-space from one side to the other, it's you really need to be operating under IFR. Otherwise, they'll give you your ADIZ squawk, and tell you "transponder observed, remain clear of the Clas Bravo airspace." That means going under it, or around it, and if you look at the chart, that means some needle-threading.
All in all, if you're heading for New England from the Carolinas, you're better off planning to go up the V1/16/93 routes east of the ADIZ/B-space complex, whether you're going IFR or VFR. Check the TEC routes in the Northeast A/FD for details.