The properties of dust in the interstellar medium (ISM) nearest the Sun are poorly understood because the low column densities of dust toward nearby stars induce little photometric reddening, rendering the grains largely undetectable. Stellar polarimetry offers one pathway to deducing the properties of this diffuse material. Here we present multi-wavelength aperture polarimetry measurements of seven bright stars chosen to probe interstellar polarization near the edge of the Local Hot Bubble (LHB) - an amorphous region of relatively low density interstellar gas and dust extending ~70-150 pc from the Sun. The measurements were taken using the HIgh Precision Polarimetric Instrument (HIPPI) on the 3.9-m Anglo-Australian Telescope. HIPPI is an aperture stellar polarimeter with a demonstrated sensitivity of 4.3 parts-per-million (ppm). Of the stars observed two are polarized to a much greater degree than the others; they have a wavelength of maximum polarization ($lambda_{max}$) of ~550 $pm$ 20 nm - similar to that of stars beyond the LHB - and we conclude that they are in the wall of the LHB. The remaining five stars have polarizations of ~70 to 160 ppm, of these four have a much bluer $lambda_{max}$, ~350 $pm$ 50 nm. Bluer values of $lambda_{max}$ may indicate grains shocked during the evolution of the Loop I Superbubble. The remaining star, HD 4150 is not well fit by a Serkowski curve, and may be intrinsically polarized.
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