We report the results of a survey of OVI 1032 absorption along the lines of sight to 25 white dwarfs in the local interstellar medium (LISM) obtained with the Far Ultraviolet Spectroscopic Explorer (FUSE). We find that interstellar OVI absorption along all sightlines is generally weak, and in a number of cases, completely absent. No OVI absorption was detected with significance greater than 2 sigma for 12 of the 25 stars, where the 1 sigma uncertainty is 4 mA, equivalent to an OVI column density of ~3 x 10^12 cm^-2. Of the remaining stars, most have column densities N(OVI) < 10^13 cm^-2 and no column densities exceed 1.7 x 10^13 cm^-2. For lines of sight to hot (T_eff > 40,000 K) white dwarfs, there is some evidence that the OVI absorption may be at least partially photospheric or circumstellar in origin. We interpret the patchy distribution of OVI absorption in terms of a model where OVI is formed in evaporative interfaces between cool clouds and the hot, diffuse gas in the Local Bubble (LB). If the clouds contain tangled or tangential magnetic fields, then thermal conduction will be quenched over most of the cloud surface, and OVI will be formed only in local patches where conduction is allowed to operate. We find an average OVI space density in the LISM of 2.4 x 10^-8 cm^-3, which is similar to, or slightly larger than, the value in the Galactic disk over kpc scales. This local density implies an average OVI column density of ~7 x 10^12 cm^-2 over a path length of 100 pc within the LB. The OVI data presented here appears to be inconsistent with the model proposed by Breitschwerdt & Schmutzler (1994), in which highly ionized gas at low kinetic temperature (~50,000 K) permeates the LB. Our survey results are consistent with the supernova-driven cavity picture of Cox & Smith (1974).
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