It is known that additive functionals of positively recurrent linear diffusions are represented as sums of independent random variables. Using this fact, i.e., by the so-called regenerative method, we can show that these functionals admit Edgeworth expansion under some conditions. For Ito diffusions, a sufficient condition is presented in terms of the coefficients of the corresponding stochastic differential equations. We also propose a bootstrap procedure, which is validated via the Edgeworth expansion. The maximal likelihood estimators of the drift coefficients of the OU processes and the CIR processes will be discussed as examples.