Você precisa definir o ambiente do shell para sair quando um teste falhar set -e
-e When this option is on, when any command fails (for any of the reasons listed in Consequences of Shell Errors or by returning an exit status greater than zero), the shell immediately shall exit, as if by executing the exit special built-in utility with no arguments, with the following exceptions: The failure of any individual command in a multi-command pipeline shall not cause the shell to exit. Only the failure of the pipeline itself shall be considered.
The -e setting shall be ignored when executing the compound list following the while, until, if, or elif reserved word, a pipeline beginning with the ! reserved word, or any command of an AND-OR list other than the last.
If the exit status of a compound command other than a subshell command was the result of a failure while -e was being ignored, then -e shall not apply to this command.
Você pode encontrar mais informações sobre as opções do bash em definir ou desmarcar opções e parâmetros posicionais
Então, seu script bash deve se tornar
#!/bin/bash
set -e
newman run ./test/postman_collection_1.json --environment ./test/postman_environment.json --bail
newman run ./test/postman_collection_2.json --environment ./test/postman_environment.json --bail