Once the bluetooth scanner is connected, the iOS device assumes this new bluetooth device which is an input device is now the main input device and therefore doesn't show the keyboard anymore as you tap for example a text field.
On your bluetooth barcode scanner: Ensure HID features for Apple iOS are enabled. HID features can normally be enabled/disabled by scanning the corresponding barcode in your bluetooth barcode scanner's manual.
Double-pressing the trigger button on your scanner may be required to bring up the iPhone keyboard for manual entry if you do not want to disconnect/reconnect your bluetooth scanner every time manual entry is required.
For the popular Zebra Motorola scanner CS3070, this is done by simply pressing the small button below the main button on the scanner, which is dedicated to bring up the iOS virtual keyboard.