The statement that bosonic strings came first and Fermionic strings came later is not exactly correct as history. Fermionic strings came almost simultaneously, when Ramond discovered the two dimensional super-conformal algebra in 1971.
Ramond style string theories did not have space-time supersymmetry (or rather, they did, but the GSO projection which was required to extract the physical spectrum was not discovered until 1976, and the proof that this projection actually leaves a sensible theory did not come until the Green-Schwarz formulation was developed in the early 1980s).
The Neveu Schwarz paper analyzes bosonic oscillations of a fermionic string, and was motivated by exploring all consistent bootstraps to find something that would work for the light mesons. The problems at the time was that a bosonic tachyon was interpreted as the experimentally known instability of the pion vacuum, so it was considered essential for a good theory. The Neveu-Schwarz sector, without the GSO projection, contains such a tachyon. Now we know that this means that the theory is sick, but back then, it was considered a good sign.
The Ramond fermions were then interpreted as bare baryons, to be dressed with the pion condensation, and this interpretation is also wrong, since baryons have a three-quark symmetry structure. The Neveu-Schwarz sector was interpreted as mesons, but they also had a tachyon (which is GSO odd and vanishes), and nothing looks like the QCD spectrum, not with the crude tools available then.
The inconsistency of Ramond-Neveu-Schwarz strings was expressed most simply by Edward Witten in the early eighties: the closed string sector of a fermionic string contains massless spin-3/2 particles, so it must couple to some space-time supercurrent in order to make sense. The graviton and spin 3/2 gravitinos must make a sensible supergravity theory. The development of supergravity was initiated to a large degree by string theory, since Scherk immediately began to investigate supergravities after GSO. He probably understood even then that the low-energy limit of superstrings would have to be some sort of supergravity.
So it is most fair to say that the development of superstrings and of bosonic strings went hand in hand, but the full perturbation series for the bosonic string was completed earlier, while a full perturbation theory of the fermionic string had to wait until the early eighties.