4D radar is increasingly attractive for robotic mapping because it provides range, azimuth, elevation, and Doppler measurements while remaining robust in adverse visibility conditions. Although recent radar and radar--inertial odometry methods have achieved promising online state estimation performance, offline global map refinement for 4D radar remains underexplored. This paper presents RAMBA, a radar bundle-adjustment framework for globally consistent 4D radar mapping. Given initial poses and radar frames from a radar--inertial odometry front-end, RAMBA jointly refines radar frame states using covariance-weighted geometric residuals, IMU preintegration factors, and radar ego-velocity constraints. The geometric residuals extend pairwise GICP to a multi-frame optimization by forming voxel-based correspondences across selected frames and weighting each residual with point covariances. To improve robustness against drift and revisits, RAMBA enforces temporal consistency during correspondence formation while explicitly supporting loop-closure constraints. Experiments on the ColoRadar and SNAIL Radar datasets show that RAMBA improves map consistency and usually enhances trajectory accuracy over radar--inertial odometry and pose-graph optimization baselines.