As per my knowledge, TTI bundling is used by UE to send uplink data mainly for VoIP data.
DRX is used to save battery life by just avoiding PDCCH reads per TTI.
If UE can sends either UL or receive DL for each TTI, then "yes" TTI bundling and DRX both should should be on at the same time but this is not the case with off. It may be UE is not using TTI bundling but DRX is on.
TTI bundling will just help to avoid re-transmission of data. When UE at cell edge or has poor channel conditions then TTI bundling will help to UE.
I am not very much comfortable with MAC features. So please correct me if I am wrong anywhere.