The "B" went away sometime in the mid/late '90s*. It's simply a "flight review." As B2N2 wrote, it does indeed have to be done with an FAA certificated flight instructor.
However, unlike much of the world, the "two-year mark" isn't a critical item. No requirements change magically from one day to the next. If you have a flight review at the three-year point then you're good for the next two years.
I have the opposite problem. I'm current in N-reg, but my EASA SEP rating expired last November - a year earlier than expected. I thought the rating had been renewed at the time I converted the German PPL(A) to an EASA license the year before. Turns out that wasn't the case. (No, I haven't been flying illegally.) This only came up because I want to add on TMG and PPL-to-TMG is easier than SPL-to-TMG. However, it's much cheaper to go SPL-to-TMG than to breath life back into the SEP rating...
*In the 90s the FAA considered implementing an annual flight review for pilots with less than 400 hours while those with more experience would be reviewed every 24 months. One frequency would have become two, so "biennial" went out the window. The change never happened.