SWift/BAT detected the first burst from 1E 1841-045 in May 2010 with intermittent burst activity recorded through at least July 2011. Here we present Swift and Fermi/GBM observations of this burst activity and search for correlated changes to the persistent X-ray emission of the source. The T90 durations of the bursts range between 18 - 140 ms, comparable to other magnetar burst durations, while the energy released in each burst ranges between (0.8-25) x 1038 erg, which is in the low side of SGR bursts. We find that the bursting activity did not have a significant effect on the persistent flux level of the source. We argue that the mechanism leading to this sporadic burst activity in IE 1841-045 might not involve large scale restructuring (either crustal or magnetospheric) as seen in other magnetar sources.