Question: I have so far only worked with WS2812 strips and understood, that the WS2813 have a backup data line. But how do I connect the first LED to my Arduino (acts as a controller)? 

Many tutorials said I should just wire the BI to V0, but doesn't this eliminate the backup functionality? So I thought about wiring both data pins to my data source? Is this a good idea?

Answer: 
This is based on a few sources including the (poor) [datasheet](https://www.elecrow.com/download/WS2813_LED_Datasheet.pdf).

My interpretation is that BIN should be connected to the *previous LED's* DIN. Then if the one LED fails, the next one will not receive any data on DIN, but it will receive data on BIN. It will switch to backup mode, where it uses the data from BIN, and ignores the data intended for the previous LED. This allows the rest of the chain to continue functioning with only one dead pixel, instead of letting the dead pixel break the chain completely. The chain will still be broken if two pixels next to each other are dead.
Based on the documentation and experimentation: do not connect them together because they are not interpreted the same way. D is the data signal and interpreted as such and B is expected to be the data signal with address shifted -1 so the addressing stays in sync. Do not connect your controller to BI. Do connect the BO at the end of one strip to the BI of the next strip in your daisy chain. If you are not chaining them together, you do not need to connect anything to BI.