There's no shortcut for this one, and that's precisely what makes routing strategy so important: business class from San Antonio to Riga always requires at least one connection, since no US carrier or airBaltic operates anything close to nonstop on this pairing. The practical answer, after years of piecing together this itinerary, is to fly American or Delta out of SAT to a major East Coast or transatlantic gateway — JFK, Philadelphia, or Charlotte work well for American, while Delta favors JFK or Atlanta — then connect onward to Riga via a European hub, most commonly through Amsterdam, Paris, or Frankfurt using a joint-venture partner, before finishing the final short hop into RIX on airBaltic or the partner carrier's regional metal. American's Flagship Business on transatlantic 777s and 787s (lie-flat with direct aisle access on the 777) is the strongest hard product available on this routing, while Delta One Suites on the A330-900 or A350 offer similarly excellent sliding doors and consistent service standards across the Atlantic leg.
The real insider move is booking the SAT-to-hub segment separately in economy or premium economy if award space in business isn't available end-to-end, then pairing it with a business class fare originating from the hub city — airlines often price these hub-originating business fares far more reasonably than the full through-fare from Texas, and it lets you take advantage of a daytime layover to shower in an American Admirals Club or Delta Sky Club before the long overnight crossing. Riga Airport itself is compact and efficient, so even if your final leg lands late, immigration and baggage rarely take more than twenty minutes, a small mercy after a long day of connections.
Late spring through early fall — May through September — is when this itinerary runs most efficiently, both because Baltic weather actually cooperates and because European hub connections see fewer weather-related delays than winter's fog and snow disruptions. Given how fragmented pricing can be across three carriers and multiple hub combinations, setting up fare alerts for this specific SAT–RIX corridor is the smartest way to catch the periodic dips before they disappear.