TLDR: adding 100pf between pin 19/SCL and ground fixed it.

I also had this problem and fixed it with the help of this thread!

First of all, I am really amazed that Paul figured this out remotely, as it is such an insidious little problem that came from a very unexpected cause. Props!!!!

I had a BNO055, Teensy audio shield and exactly the same weird crash symptoms. Good data for a few seconds, then a weird crash to all ".06" values.
Remove the I2S1 line and everything was good.

I tried these things:
- adding various sizes of capacitors to the BNO055 power supply. No effect.
- shielding the sensor with some grounded copper tape (wrapped in non-conductive tape) but that did nothing. No effect!
- placing some grounded and insulated copper shielding near the MCLK pin (11). Nope.
- thinking that the 11Mhz must be leaking on the SDA/SCL lines, I added a 10pf bypass between pin 18 (SDA) and ground. No effect.
- then I thought: let's try 100pf (Xc about 145 ohms at 11Mhz) between pin 19 (SCL) and ground SUCCESS!

This problem was worse than catching a mouse in a fifty room mansion, so I am extremely impressed a Paul's answer! It's truly exceellent troubleshooting. Thank you.

Daniel

PS: I did see something in the Adafruit manual for the BNO055 that said something like "do watch out RF square waves, as the sensor does not like them and will give weird results!"