A bidirectional disappearing plug member and plug assembly is capable of blocking pressurized fluid flow from opposing axial directions in a flowbore. In a preferred embodiment, the plug member, which blocks flow through the flowbore, may be readily and at least partially dissolved through the application of at least one pressurization and depressurization within a tubing string above the plug assembly. Construction of the plug assembly permits the plug member to be conveniently emplaced in a fluid-filled wellbore by permitting fluid flow around the plug member during the emplacement process. The plug member may then be secured within the plug assembly to block fluid flow from either axial direction. Operation of a plug rupture sleeve or mandrel, for at least partially dissolving the plug member, may be controlled by a ratchet assembly or linear indexing apparatus requiring multiple pressurizations and depressurizations before the plug member is exposed to wellbore fluids and thereby at least partially dissolved.