We introduce the notion of an $n$-trivialization and a compatible curving and construct the splitting of bundle gerbe modules to define the twisted Chern classes and the twisted Chern character for bundle gerbe modules in terms of algebraic topology. Moreover, we prove that the latter coincides with the twisted Chern character due to Bouwknegt-Carey-Mathai-Murray-Stevenson  if the bundle gerbe is given an $n$-trivialization and a compatible curving.
"On the splitting principle of bundle gerbe modules." Osaka J. Math. 44 (1) 231 - 246, March 2007.