My boyfriend thinks that someone that we are actively trying to get a retraining order against has bugged my computer and asked me to record the search history on my tablet, does that really do anything or does he just want me to show him my search history?
Honestly, he just wants you to show him your search history. I know you might be thinking, "that's rather blunt," but the honest truth is if someone has bugged your COMPUTER (assuming its separate from your tablet) and you record search history on your TABLET it will do nothing except give whoever gets the history a detailed map of every search you conduct online on that device. (I will post another answer that assumes that the computer and tablet are the same device below).
Assuming they are the same device, if your tablet's bugged, the advice your boyfriend gave you is what you should definitely NOT do. If you do record your search history, this page might show up, alerting anyone who has bugged your computer that you know they have done so and telling them that you are recording your searches. They'll just delete the search history after they're done first of all, and second of all if you think you're being bugged you need to report the incident to the local police department immediately. You might even hire an investigator to determine who bugged your device. That's the most reliable method as far as I'm aware.