I would like recommend the following references for estimating the Zeros of Bessel Functions:
Abramowitz, M. and Stegun, I. A. (Eds.). "Zeros." §9.5 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 370-374, 1972.
Goodwin, E. T. and Staton, J. "Table of "J_0(j_(0,n)r)." Quart. J. Mech. Appl. Math. 1, 220-224, 1948.
Olver, F. W. J. (Ed.). "Zeros and Associated Values." Royal Society Mathematical Tables, Vol. 7: Bessel Functions. Cambridge, England: Cambridge University Press, 1960.