Optical spectroscopy of the highly collimated bipolar nebulae He 2-25, Th 2-B and 19W32 is presented. He 2-25 and Th 2-B are found to have very dense (N_e~10^7 cm^-3) cores characterized by emission lines of low- to intermediate-ionization species, including rich [FeII] emission. The Hα profiles present broad non-Gaussian wings. These spectral characteristics are common to a subclass of bipolar planetary nebulae (PNe), including the well-studied M 2-9, and closely resemble those of interacting binary systems such as symbiotic stars. The core spectrum of 19W32 shows only Hα and [NII]lambda6583 in emission, and is dominated by a stellar continuum from a relatively cold star whose classification is tentatively given as between K0 and M2. Provision of a better classification and determination of whether this star is indeed physically associated with the nebula would be important to understand the nature of these objects and to test the hypothesis of binarity for the formation of bipolar planetary nebulae. The possible classification of this class of objects as proto-PNe or symbiotic stars is discussed.