We present a mid-infrared (IR) sample study of nearby ultraluminous X-ray sources (ULXs) using multiepoch observations with the Infrared Array Camera (IRAC) on the Spitzer Space Telescope. Spitzer/IRAC observations taken after 2014 were obtained as part of the Spitzer Infrared Intensive Transients Survey. Our sample includes 96 ULXs located within 10 Mpc. Of the 96 ULXs, 12 have candidate counterparts consistent with absolute mid-IR magnitudes of supergiants, and 16 counterparts exceeded the mid-IR brightness of single supergiants and are thus more consistent with star clusters or non-ULX background active galactic nuclei. The supergiant candidate counterparts exhibit a bimodal color distribution in a Spitzer/IRAC color-magnitude diagram, where "red" and "'blue" ULXs fall in IRAC colors [3.6]-[4.5]~0.7 and [3.6]-[4.5]~0.0, respectively. The mid-IR colors and absolute magnitudes of four "red" and five "blue" ULXs are consistent with those of supergiant B[e] (sgB[e]) and red supergiant (RSG) stars, respectively. Although "blue," RSG-like mid-IR ULX counterparts likely host RSG mass donors; we propose that "red" counterparts are ULXs exhibiting the "B[e] phenomenon" rather than hosts of sgB[e] mass donors. We show that the mid-IR excess from the "red" ULXs is likely due to thermal emission from circumstellar or circumbinary dust. Using dust as a probe for total mass, we estimate mass-loss rates of dM/dt~1x10^-4^M_{sun}_/yr in dust-forming outflows of red ULXs. Based on the transient mid-IR behavior and its relatively flat spectral index, {alpha}=-0.19+/-0.1, we suggest that the mid-IR emission from Holmberg IX X-1 originates from a variable jet.