Optical networks are evolving toward ultrawide bandwidth and autonomous operation. In this scenario, it is crucial to accurately model and control optical power evolutions (OPEs) through optical amplifiers (OAs), as they directly affect the signal-to-noise ratio and fiber nonlinearities. However, a fundamental contradiction arises between the complex physical phenomena in optical transmission and the required precision in network control. Traditional theoretical methods underperform due to ideal assumptions, while data-driven approaches entail exorbitant costs associated with acquiring massive amounts of data to achieve the desired level of accuracy. In this work, we propose a Bayesian inference framework (BIF) to construct the digital twin of OAs and control OPE in a data-efficient manner. Only the informative data are collected to balance the exploration and exploitation of the data space, thus enabling efficient autonomous-driving optical networks (ADONs). Simulations and experiments demonstrate that the BIF can reduce the data size for modeling erbium-doped fiber amplifiers by 80% and Raman amplifiers by 60%. Within 30 iterations, the optimal controlling performance can be achieved to realize target signal/gain profiles in links with different types of OAs. The results show that the BIF paves the way to accurately model and control OPE for future ADONs.