Just saw your post. If you're still looking for a Modbus RTU (RS323 or RS485) to Bluetooth converter to connect to mobiles, IOTize have a product called TapNPass that might help you: https://www.iotize.com/tapnpass-line.html
It includes an app for Android and iOS devices that provides you either a simple terminal or an interface for selecting and reading/writing data to Modbus registers.
If you need to create an interface dedicated to a specific task, you can also configure the TapNPass and create your own HMI apps for Android or iOS devices.
You can do it over Wi-Fi instead of over Bluetooth.
Wi-Fi ModBus gateways are available on the market.
It does not have to be a wireless modem in the environment. You can connect to Wi-Fi network with "Access Point" mode of Wi-Fi Modbus Gateways and view the data of your device via mobile application.