We present a mid-infrared (IR) sample study of nearby ultraluminous X-ray sources (ULXs) using multi-epoch 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 (SPIRITS). 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 (AGN). The supergiant candidate counterparts exhibit a bi-modal color distribution in a Spitzer/IRAC color-magnitude diagram, where red and blue ULXs fall in IRAC colors $[3.6] - [4.5]sim0.7$ and $[3.6] - [4.5]sim0.0$, respectively. The mid-IR colors and absolute magnitudes of 4 red and 5 blue ULXs are consistent with that of supergiant B[e] (sgB[e]) and red supergiant (RSG) stars, respectively. While blue, RSG-like mid-IR ULX counterparts likely host RSG mass donors, we propose the 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 $dot{M}sim1times10^{-4}$ M$_odot$ yr$^{-1}$ in dust-forming outflows of red ULXs. Based on the transient mid-IR behavior and its relatively flat spectral index, $alpha=-0.19pm0.1$, we suggest that the mid-IR emission from Holmberg IX X-1 originates from a variable jet.
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