In the TV series Edit
Beth is portrayed by Kristen Gutoskie.
A Martha affiliated with Jezebel's, she is first seen at the brothel trading with Nick bottles of alcoholic beverages and additional contraband for other illicit goods, such as prescription drugs and pregnancy tests that are used by the customers or working girls of the brothel. Nick formally comments the trade with "the Eyes thank you for your service".
She is (or used to be) in a sexual relationship with Nick, who refuses her advances because of his interest for Offred.
Beth was a very talented chef in her past life, mentioning her pesto recipe got her a James Beard nomination after getting fresh basil from Nick.
Another night, when Nick and Beth are meeting again in the Jezebel's kitchen, Nick is curious if she "asked around at the bar" that "nobody's planning anything stupid", and Beth replies that the girls in here are not "in the shape for a rebellion". She warns Nick about the dangerous consequences of "poking around, asking questions", or "being sweet" with a handmaid. 
Beth is able to gain information from the rebel network in spite of her obvious relationship to an Eye.
Nick trades on behalf of the Eyes, i.e. the Eyes' administration tolerates drug trafficking (in a certain measure).
Since the Eyes are involved in trafficking here and due to the obviously frank and trustful contact between Nick, Beth and the "bar people", it is unlikely that Nick or Beth have an official order to spy for the Eyes inside Jezebel's, and thus their interest for rebel activities is solely private. This could mean that they're both trusted parts of the Mayday network.