Stellar-feedback-driven outflows are predicted to play a fundamental role in the baryon cycle of low-mass galaxies. However, observational constraints of winds in nearby dwarf galaxies are limited, as outflows are transient, intrinsically low surface brightness features and thus difficult to detect. Using deep Hα observations, we search for winds in a sample of 12 nearby dwarfs (M* ∼ 107-109.3 M☉) that host ongoing or recent starbursts. We detect features that we classify as winds in six galaxies, fountain candidates in five galaxies, and diffuse interstellar medium (ISM) in one system. Winds are found preferentially in galaxies with centrally concentrated star formation, while fountains are found in galaxies with spatially distributed star formation. We suggest that the concentration of star formation is a predictor for whether a low-mass galaxy will develop a wind. The spatial extent of all detected ionized gas is limited (<1/10 virial radius) and would still be considered the ISM by cosmological simulations. Our observations suggest that the majority of material expelled from dwarfs does not escape to the intergalactic medium but remains in the halo and may be recycled to the galaxies. Derived mass-loading factors range from 0.2 to 7 (with only a weak dependency on circular velocity or stellar mass), in tension with higher values in simulations needed to reproduce realistic low-mass galaxies and resolve discrepancies with ΛCDM. The sample is part of the panchromatic STARBurst IRegular Dwarf Survey-STARBIRDS-designed to characterize the starburst phenomenon in dwarf galaxies. We also report a previously uncatalogued nearby galaxy (J1118+7913).