We present a search for a Higgs-like particle $\phi$ decaying into $b\bar{b}$ produced in association with $b$ quarks in $p\bar{p}$ collisions. The event sample corresponds to 5.4 $\text{fb}^{-1}$ of integrated luminosity collected with the CDF II detector at the Tevatron collider using a single $b$ tagged jet trigger. We search for an enhancement in the mass of the two leading jets in event with at least three jets identified as coming from $b$ quarks. A data-driven procedure is applied to estimate the dijet mass spectrum of the non-resonant multijet background, which has been used to measure the production cross-section of the $Z$ decaying into $b\bar{b}$ in the same sample but with at least two b-jets. We set one of the most stringent upper limits on $\sigma(p\bar{p} \rightarrow \phi b) \times \mathcal{B}(\phi \rightarrow b\bar{b})$ in the $100-300~\text{GeV/c}^2$ mass range.