We present the Bayesian Asteroseismology data Modeling (BAM) pipeline, an automated asteroseismology pipeline that returns global oscillation parameters and granulation parameters from the analysis of photometric time series. BAM also determines whether a star is likely to be a solar-like oscillator. We have designed BAM to specially process K2 light curves, which suffer from unique noise signatures that can confuse asteroseismic analysis, though it may be used on any photometric time series-including those from Kepler and TESS. We demonstrate that the BAM oscillation parameters are consistent within ~1.53%(random) +/-0.2%(systematic) and 1.51%(random) +/-0.6%(systematic) for {nu}_max_ and {Delta}{nu} with benchmark results for typical K2 red giant stars in the K2 Galactic Archaeology Program's (GAP) Campaign 1 sample. Application of BAM to 13,016 K2 Campaign 1 targets not in the GAP sample yields 104 red giant solar-like oscillators. Based on the number of serendipitous giants we find, we estimate an upper limit on the average purity in dwarf selection among C1 proposals of ~99%, which could be lower when considering incompleteness in BAM detection efficiency and proper-motion cuts specific to C1 Guest Observer proposals.