Dell XPS 13 (9370) Bluetooth issues

I had the same problem, and I think it improved by updating the Bluetooth firmware using the files included in the newest Windows driver. My MD5s:

sonic@sonic-XPS-13-9370:/lib/firmware/qca$ md5sum *usb*302*
067fb95e8501bad2683df07d23539e7d  nvm_usb_00000302.bin
b3e2784b16b5b0cf5defa7eb9115956d  nvm_usb_00000302.bin_orig
c9d6334b547a92817458de10243f398c  rampatch_usb_00000302.bin
86c377ab7b2c24cc12cea5e79f71d610  rampatch_usb_00000302.bin_orig

By the way, an easier workaround was to unplug the power and do a suspend/resume cycle.
And at least mine is a 1435 Killer.

Update to Sven Killig's answer for Dell XPS 9370 on Ubuntu 18.04:

Driver:

https://www.dell.com/support/home/uk/en/ukbsdt1/drivers/driversdetails?driverId=1JVK3

Files to override:

AthrBT_0x00000302.dfu (size 40876) -> rampatch_usb_00000302.bin (size 32940)
ramps_0x00000302_48.dfu (size 1982) -> nvm_usb_00000302.bin (size 1953)

Listing after copy:

067fb95e8501bad2683df07d23539e7d  /lib/firmware/qca/nvm_usb_00000302.bin
b3e2784b16b5b0cf5defa7eb9115956d  /lib/firmware/qca/nvm_usb_00000302.bin.orig
47ed34d8b6af11d71036aa44314e32d3  /lib/firmware/qca/rampatch_usb_00000302.bin
86c377ab7b2c24cc12cea5e79f71d610  /lib/firmware/qca/rampatch_usb_00000302.bin.orig