Bastion asked Rahm to dispose of him in the first panel here. Ashley mentioned that she originally planed for Bastion to kill Elan because Bastion "takes betrayal personally." My guess is that Bastion considers Quigley to have betrayed the plot, too (even if Quigley never talked to Bastion directly) and he doesn't want to take any chances with Quigley possibly causing problems in the future, so he wants Quigley to die. It's probably more a matter of not wanting to take any chances than actually expecting Quigley to cause problems.