Is $\lim_{t \rightarrow \infty} B_t = 0$ at equilibrium in classical monetary model, where $B_t$ represents bond holding?
In general, no.

As you correctly say, No-Ponzi and Transversality imply that the NPV of real bond holdings go to zero. Since we (in general) have not pinned down inflation paths, this does not imply $\lim_t B_t = 0$, as you correctly suspect.

If you can provide more information about what model exactly you work on or the situation you're looking at, I could update my answer.