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Interest in topological states of matter burgeoned over a decade ago with the theoretical prediction and experimental detection of topological insulators, especially in bulk three-dimensional insulators that can be tuned out of it by doping. Their superconducting counterpart, the fully-gapped three-dimensional time-reversal-invariant topological superconductors, have evaded discovery in bulkintrinsic superconductorsso far. The recently discovered topological metalβ-PdBi₂is a unique candidate for tunable bulk topological superconductivity because of its intrinsic superconductivity and spin-orbit-coupling. In this work, we provide experimental transport signatures consistent with fully-gapped 3D time-reversal-invariant topological superconductivity in K-dopedβ-PdBi₂. In particular, we find signatures of odd-parity bulk superconductivity via upper-critical field and magnetization measurements— odd-parity pairing can be argued, given the band structure ofβ-PdBi₂, to result in 3D topological superconductivity. In addition, Andreev spectroscopy reveals surface states protected by time-reversal symmetry which might be possible evidence of Majorana surface states (Majorana cone). Moreover, we find that the undoped bulk system is a trivial superconductor. Thus, we discoverβ-PdBi₂as a unique bulk material that, on doping, can potentially undergo an unprecedented topological quantum phase transition in the superconducting state.