This should follow from [Minsky's work][1] on a priori bounds for surface groups, which is used in the proof of the ending lamination conjecture. 
The [punctured torus case][2] is simpler and more explicit (see Theorem 4.1 and equations 4.4 and 4.5). 


  [1]: http://front.math.ucdavis.edu/0302.5208
  [2]: http://www.ams.org/mathscinet-getitem?mr=1689341