Rotational structures have been measured using the Jurogam II and GAMMASPHERE arrays at low spin following the 155Gd(α,2n)157Dy and 148Nd(12C,5n)155Dy reactions at 25 and 65 MeV, respectively. We report high-K bands, which are conjectured to be the first candidates of a Kπ=2+γ vibrational band, built on the [505]11/2− neutron orbital, in both odd-A155,157Dy isotopes. The coupling of the first excited K=0+ states or the so-called β vibrational bands at 661 and 676 keV in 154Dy and 156Dy to the [505]11/2− orbital, to produce a Kπ=11/2− band, was not observed in both 155Dy and 157Dy, respectively. The implication of these findings on the interpretation of the first excited 0+ states in the core nuclei 154Dy and 156Dy are also discussed.