it looks like there may be something wrong with the connection: the activity you see is probably due to the master (the BBB) trying to communicate to the slave.
Can you try
grep "97c\|978\|980\|984" $PINS
just to double check that the pinmuxer settings are ok?
You should get
pin 94 (44e10978) 00000073 pinctrl-single
pin 95 (44e1097c) 00000073 pinctrl-single
pin 96 (44e10980) 00000073 pinctrl-single
pin 97 (44e10984) 00000073 pinctrl-single
Also, while Bela is not running, you could try to connect your I2C device to the i2c2 bus. There you should see something like this when nothing is connected:
# i2cdetect -r -y 2
0 1 2 3 4 5 6 7 8 9 a b c d e f
00: -- -- -- -- -- -- -- -- -- -- -- -- --
10: -- -- -- -- -- -- -- -- 18 -- -- -- -- -- -- --
20: -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
30: -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
40: -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
50: -- -- -- -- UU UU UU UU -- -- -- -- -- -- -- --
60: -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
70: -- -- -- -- -- -- -- --
Which is the audio codec for Bela. If you plug in your device, then the above should change to show up your device.
Running another I2C device on the same bus as the one used for the Bela audio codec is fine as long as you make sure that you do not communicate with that device when a Bela program starts ( the codec is configured every time the Bela program is started).