Rinse black-eyed peas and pick through the beans and discard any debris or beans that are shriveled or discolored.
Add the bacon to the Instant Pot and press the SAUTE button. Change the heat to custom and adjust to MEDIUM heat. When the display reads "HOT” continue to cook the bacon for 4-5 minutes. Press CANCEL on the Instant Pot.
Stir in the beans, ham, water, chicken bouillon, Cajun seasoning, and thyme. Stir to combine. Put the lid on and lock it into place. Make sure the vent is sealed.
Press PRESSURE COOK. Select HIGH and adjust the time to 17 minutes.
Allow the steam pressure to naturally release for 15 minutes. Manually release any remaining pressure. Unlock and remove the lid. Salt and pepper to taste.
Serve.