You can just buy a very cheap module which does this directly, commonly called HC-06 or HC-05

e.g. https://www.aliexpress.com/item/33010159305.html?spm=a2g0o.p...

You can, of course, DIY something easily enough but you can also purchase devices like this off the shelf. Needing to make legacy RS232 devices wirelessly available is a common problem in industry. Search for "wireless RS232 gateway" and you should be able to find a ton of stuff.

If you still want to DIY, an ESP32 (BLE and Wi-Fi capable microcontroller) board, and an RS232 to logic-level breakout board should be all you need. Again, I'm sure if you search, you'll find existing projects doing exactly this.

If it's not actually at RS232 voltage levels and Classic Bluetooth is enough, then something like this will work just fine: https://www.amazon.com/Wireless-Bluetooth-Transceiver-Integr...

You may find esp-link interesting: https://github.com/jeelabs/esp-link I've built a WiFi<->RS232 bridge using the firmware, ESP8266 and a UART<->RS232 converter module. All hardware is very cheap.