There is a later version of the Broadcom Bluetooth drivers on the Dell support page. Navigate to the support page then go to support by product and select the Dell XPS 13 9343 (Laptop), then go to the drivers section. It will default to "Windows 8.1, 64-bit". Change it to "Windows 10, 64-bit", then go to the network section and you will find it labeled as "Dell Wireless 1560 Bluetooth Driver" which is version 12.0.1.653. Although it is labeled for the DW1560, I believe it has firmwares for all Broadcom devices.
There is a later version of the Broadcom Bluetooth drivers on the Dell support page. Navigate to the support page then go to support by product and select the Dell XPS 13 9343 (Laptop), then go to the drivers section. It will default to "Windows 8.1, 64-bit". Change it to "Windows 10, 64-bit", then go to the network section and you will find it labeled as "Dell Wireless 1560 Bluetooth Driver" which is version 12.0.1.653. Although it is labeled for the DW1560, I believe it has firmwares for all Broadcom devices.
Quick link: http://www.dell.com/support/home/ca/en/cadhs1/Drivers/DriversDetails?driverId=PJXKF&fileId=3474957926&osCode=WT64A&productCode=xps-13-9343-laptop&languageCode=en&categoryId=NI