  The search for exotic Higgs decays are an essential probe of new physics. In
particular, the small width of the Higgs boson makes its decay uniquely
sensitive to the existence of light hidden sectors. Here we assess the
potential of an exotic Higgs decay search for h -> 2X -> bbmumu to constrain
theories with light CP-even (X = s) and CP-odd (X = a) singlet scalars in the
mass range of 15 to 60 GeV. This decay channel arises naturally in many
scenarios, such as the Standard Model augmented with a singlet, the
two-Higgs-doublet model with a singlet (2HDM+S) -- which includes the
Next-to-Minimal Supersymmetric Standard Model (NMSSM) -- and in hidden valley
models. The 2b2mu channel may represent the best discovery avenue for many
models. It has competitive reach, and is less reliant on low-pT b- and
tau-reconstruction compared to other channels like 4b, 4tau, and 2tau2mu. We
analyze the sensitivity of a 2b2mu search for the 8 and 14 TeV LHC, including
the HL-LHC. We consider three types of analyses, employing conventional
resolved b-jets with a clustering radius of R ~ 0.4, thin b-jets with R=0.2,
and jet substructure techniques, respectively. The latter two analyses improve
the reach for m_X ~ 15 GeV, for which the two b-jets are boosted and often
merged. We find that Br(h -> 2X -> 2b2mu) can be constrained at the few x 10^-5
level across the entire considered mass range of X at the HL-LHC. This
corresponds to a 1 - 10% reach in Br(h->2X) in 2HDM+S models, including the
NMSSM, depending on the type of Higgs Yukawa couplings.
