Hello AldoXr,
Thanks for reaching out to the Apple Support Communities. From your message I understand you’re having trouble with Bluetooth connectivity since updating to iOS 13.1. Not to worry, I’m happy to help.
iOS 13.2 has recently been released. Keeping your iPhone up-to-date ensures that you have the latest security updates and performance enhancements. There have also been some corrections made with Bluetooth. You can read about all the updates for iOS 13 here: About iOS 13 Updates.
Before updating your iPhone be sure to create a backup of your iPhone data. Having a backup of your data is like having an insurance policy, you don’t plan on using it, but it’s great to have if you need it. Here’s how to back up your iPhone: How to back up your iPhone, iPad, and iPod touch.
Once the backup is complete, please install the update. You can update your iPhone using either wireless over-the-air updating or update using your computer: Update your iPhone, iPad, or iPod touch.
Let us know how the Bluetooth on your iPhone performs on iOS 13.2.