What is the 'bump' near $M_{\mu\mu}\approx 30\text{ GeV}$

I would say that this is not physics but rather a detector/instrumentation effect. More specifically this could be due to the fact that the grey distribution is one that is collected with a high-$p_\mathrm{T}$ muon trigger. These triggers kick in at around 15-20 GeV. Depending on the topology of the event (angles) the invariant mass would of this range as well.

It is instructive to have a look at plots using different triggers.

1) in fact in the plot you reference there a a number of different trigger configurations (setup specifically for the resonances plus two general low/high pt trigger paths) superimposed over each other.

2) here's a similar plot with muons trigger that do not have a pt threshold. notice the lack of a bump in the region you specified.

3) here a similar plot by ATLAS (from 2010) where only events passing the high pt muon threshold are plotted. Notice how the bump seems to reappear.

If you go to the preprint of CMS at this link the uncorrected dimuon plot is shown in fig1 on the left. The bump is there. The ratio of data to Monte Carlo is correctly around 1. From the monte carlo it is seen that the 30GeV bump comes from collective QCD related effects.

Figure 1: The observed dimuon (left) and dielectron (right) invariant mass spectra. No corrections are applied to the distributions. The points with error bars represent the data, while the various contributions from simulated events are shown as stacked histograms. By "EWK" we denote W to lepton neutrino and diboson production. The "QCD" contribution results from processes associated with QCD and could be genuine or misidentied leptons. The lower panels show the ratios between the measured and the simulated distributions including the statistical uncertainties from both.

The dielectron distribution does not show the bump, a good reason to accept that it is misidentification and kinematic balance effect.