We report the results of a survey of O vi \lambda 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 O vi absorption along all sightlines is generally weak , and in a number of cases , completely absent . No O vi absorption was detected with significance greater than 2 \sigma for 12 of the 25 stars , where the 1 \sigma uncertainty is \sim 4 mÅ , equivalent to an O vi column density of \sim 3 \times 10 ^ { 12 } cm ^ { -2 } . Of the remaining stars , most have column densities N ( O vi ) < 10 ^ { 13 } cm ^ { -2 } and no column densities exceed 1.7 \times 10 ^ { 13 } cm ^ { -2 } . For lines of sight to hot ( T _ { eff } > 40 , 000 K ) white dwarfs , there is some evidence that the O vi absorption may be at least partially photospheric or circumstellar in origin . We interpret the “ patchy ” distribution of O vi absorption in terms of a model where O vi 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 O vi will be formed only in local “ patches ” where conduction is allowed to operate . We find an average O vi space density in the LISM of 2.4 \times 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 O vi column density of \sim 7 \times 10 ^ { 12 } cm ^ { -2 } over a path length of 100 pc within the LB . The O vi data presented here appears to be inconsistent with the model proposed by Breitschwerdt & Schmutzler ( 12 ) , in which highly ionized gas at low kinetic temperature ( \sim 50 , 000 K ) permeates the LB . Our survey results are consistent with the supernova-driven cavity picture of Cox & Smith ( 19 ) for the LB , and in particular , the recent model by Cox & Helenius ( 17 ) for the creation of cool clouds in the LB by magnetic flux tubes , and their subsequent magnetic shielding from conduction .