Data-driven control approaches for the minimization of energy consumption of buildings have the potential to significantly reduce deployment costs and increase the uptake of advanced control in this sector. A number of recent approaches based on the application of Willems' fundamental lemma for data-driven controller design from input/output measurements are very promising for deterministic linear time-invariant (LTI) systems. This article proposes a systematic way to handle unknown measurement noise and measurable process noise, and extends these data-driven control schemes to adaptive building control via a robust bilevel formulation, whose upper level ensures robustness and whose lower level guarantees prediction quality. Corresponding numerical improvements and an active excitation mechanism are proposed to enable a computationally efficient reliable operation. The efficacy of the proposed scheme is validated by a multizone building simulation and a real-world experiment on a single-zone conference building on the ecole Polytechnique Federale de Lausanne (EPFL) campus. The real-world experiment includes a 20-day nonstop test, where, without extra modeling effort, our proposed controller improves 18.4% energy efficiency against an industry-standard controller while also robustly ensuring occupant comfort.