Birmingham, Alabama, is an unlikely beachhead for an assault on the U.S. banking market, but it suits José María García Meyer, the general leading the campaign on behalf of Spain’s Banco Bilbao Vizcaya Argentaria, just fine.

García Meyer was instrumental in building BBVA’s Bancomer subsidiary into the largest bank in Mexico over the past decade through opportunistic acquisitions and the application of the Spanish bank’s vaunted technology and marketing expertise. Now he’s determined to pull off a similar feat at BBVA Compass, the bank’s fast-growing U.S. unit, which he chairs. BBVA began dipping its toe into the U.S. market in 2004 with the $17 million purchase of tiny, six-branch Valley Bank in Southern California, then snapped up a few small Texas banks over the next two years. Modest beginnings, to be sure, but enough of a base to enable BBVA to gain...