Control barrier functions (CBFs) provide a tractable mechanism for enforcing safety constraints in robotic systems, but their practical performance depends strongly on the choice of class-K function parameters. Under input constraints, conservative parameters often preserve feasibility at the cost of slow progress, whereas aggressive parameters can make the CBF-based optimization infeasible or unsafe. This paper proposes Online Adaptive CBF (OA-CBF), a framework for adapting CBF parameters at runtime. We introduce the notion of locally validated CBF parameters, which certify candidate parameters over a finite prediction horizon, and show that safety is preserved when such validation is maintained over successive update intervals. To identify locally validated parameters efficiently, OA-CBF trains a probabilistic ensemble neural network to evaluate queried CBF parameters rather than directly predict a single parameter. A graph-attention encoder represents variable-size obstacle environments, an epistemic uncertainty gate calibrated by conformal prediction rejects unreliable predictions, and a distributionally robust CVaR condition screens aleatoric risk. Among the verified candidates, OA-CBF selects the parameter with the best predicted progress metric and applies it through either an MPC-CBF or CBF-QP safety filter. Simulation studies on dynamic unicycle, planar and three-dimensional quadrotor, kinematic bicycle, and VTOL quadplane benchmarks show that OA-CBF reduces the conservatism of fixed-parameter CBF controllers while maintaining low collision and infeasibility rates.