Variations in stellar flux can potentially overwhelm the photometric signal of a transiting planet. Such variability has not previously been well-characterized in the ultraviolet lines used to probe the inflated atmospheres surrounding hot Jupiters. Therefore, we surveyed 38 F-M stars for intensity variations in four narrow spectroscopic bands: two enclosing strong lines from species known to inhabit hot Jupiter atmospheres, C.II {lambda}{lambda}1334, 1335 and SiIII{lambda}1206; one enclosing SiIV {lambda}{lambda}1393, 1402; and 36.5{AA} of interspersed continuum. For each star/band combination, we generated 60s cadence lightcurves from archival Hubble Space Telescope Cosmic Origins Spectrograph and Space Telescope Imaging Spectrograph time-tagged photon data. Within these lightcurves, we characterized flares and stochastic fluctuations as separate forms of variability. Flares: we used a cross-correlation approach to detect 116 flares. These events occur in the time-series an average of once per 2.5hr, over 50% last 4 minutes or less, and most produce the strongest response in SiIV. If the flare occurred during a transit measurement integrated for 60 minutes, 90/116 would destroy the signal of an Earth, 27/116 Neptune, and 7/116 Jupiter, with the upward bias in flux ranging from 1% to 109% of quiescent levels. Fluctuations: photon noise and underlying stellar fluctuations produce scatter in the quiescent data. We model the stellar fluctuations as Gaussian white noise with standard deviation {sigma}_x_. Maximum likelihood values of {sigma}_x_ range from 1% to 41% for 60s measurements. These values suggest that many cool stars will only permit a transit detection to high confidence in ultraviolet resonance lines if the radius of the occulting disk is >~1R_J_. However, for some M dwarfs this limit can be as low as several R_{oplus}_.