Long-duration gamma-ray bursts (GRBs) are indisputably related to star formation, and their vast luminosity in gamma rays pin-points regions of star formation independent of galaxy mass, out to the epoch of re-ionisation. As such, GRBs provide a unique tool for studying star forming galaxies out to high-z independent of luminosity. Most of our understanding of the properties of GRB hosts (GRBHs) comes from optical and near-infrared follow-up observations, and we therefore have relatively little knowledge of the fraction of dust-enshrouded star formation that resides within GRBHs. Currently ~20% of GRBs show evidence of significant amounts of dust within their host galaxy along the GRB line of sight, and these GRBs tend to reside within redder and more massive galaxies than GRBs with optically bright afterglows. In this paper we present Herschel observations of five GRBHs with evidence of being dust-rich, targeted to understand the properties of the dust attenuation within GRBs better. Despite the sensitivity of our Herschel observations, only one galaxy in our sample was detected (GRBH 070306), for which we measure a total star formation rate of ~100 M⊙ yr-1, and which had a relatively high stellar mass (log[M*] = 10.34+0.09-0.04. Nevertheless, when considering a larger sample of GRBHs observed with Herschel, it is clear that stellar mass is not the only factor contributing to a Herschel detection, and significant dust extinction along the GRB sightline (AV,GRB> 1.5 mag) appears to be a considerably better tracer of GRBHs with a high dust mass. This suggests that the extinguishing dust along the GRB line of sight lies predominantly within the host galaxy ISM, and thus those GRBs with AV,GRB> 1 mag but with no host galaxy Herschel detections are likely to have been predominantly extinguished by dust within an intervening dense cloud.