Individuals taking an old-new recognition memory test differ widely in their bias to respond "old," ranging from strongly conservative to strongly liberal, even without any manipulation intended to affect bias. Kantner and Lindsay (2012) found stability of bias across study-test cycles, suggesting that bias is a cognitive trait. That consistency, however, could have arisen because participants perceived the two tests as being part of the same experiment in the same context. In the present study, we tested for stability across two recognition study-test procedures embedded in markedly different experiments, held weeks apart, that participants did not know were connected. Bias showed substantial cross-situational stability. Moreover, bias weakly predicted identifications on an eyewitness memory task and accuracy on a go-no-go task. Although we found little in the way of relationships between bias and five personality measures, these findings suggest that response bias is a stable and broadly influential characteristic of recognizers.