We present our observations of the optical intra-day variability (IDV) in $gamma$-ray BL Lac object Mrk 501. The observations were run with the 1.02 m and 2.4 m optical telescopes at Yunnan Observatories from 2005 April to 2012 May. The light curve at the $R$ band on 2010 May 15 passes both variability tests (the $F$ test and the ANOVA test). A flare within the light curve on 2010 May 15 has a magnitude change $Delta m = 0.03 pm 0.005_{rm{stat}} pm 0.007_{rm{sys}}$ mag, textbf{a darkening timescale of $tau_{rm{d}}=$ 26.7 minutes}, and an amplitude of IDV $Amp=2.9% pm0.7%$. A decline textbf{described by 11 consecutive flux measurements} within the flare can be fitted linearly with a Pearsons correlation coefficient $r = 0.945$ at the confidence level of $> 99.99%$. Under the assumptions that the IDV is tightly connected to the mass of the black hole, textbf{and that the flare duration, being two times $tau_{rm{d}}$, is representative of the minimum characteristic timescale, we can derive upper bounds to the mass of the black hole}. In the case of the Kerr black hole, the timescale of $Delta t_{rm{min}}^{rm{ob}}=$ 0.89 hours gives $M_{bullet}la 10^{9.20} M_{odot}$, which is consistent with measurements reported in the literature. This agreement indicates that the hypothesis about $M_{bullet}$ and $Delta t_{rm{min}}^{rm{ob}}$ is consistent with the measurements/data.
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