Data products from the Advanced Camera for Surveys Virgo cluster survey are used to understand the bulge star formation history in early-type galaxies at redshifts z ≳2. A new technique is developed whereby observed high-redshift age-metallicity relationships are utilized to constrain the typical formation epochs of metal-rich or 'bulge' globular clusters. This analysis supports a model where massive Virgo galaxies underwent an extremely intense mode of bulge globular cluster formation at z ∼ 3.5 that was followed by an era of significant bulge growth and little globular cluster production. Intermediate-mass galaxies showed a less intense period of globular cluster formation at z ∼ 2.5 that was synchronized with the bulk of bulge star growth. The transition between the massive and intermediate-mass galaxy star formation modes occurs at a galaxy stellar mass of Mstellar ∼ 3 × 1010 M⊙, the mass where many other galaxy properties are observed to change. Dwarf early-type galaxies in Virgo may have experienced no significant period of bulge globular cluster formation, thus the intense starbursts associated with globular cluster formation may be difficult to directly observe at redshifts z ≲ 4. Although the above conclusions are preliminary because they are based upon uncertain relationships between age and metallicity, the technique employed will yield more stringent constraints as high-redshift galaxy observations and theoretical models improve.