First of all I believe your question is more a hardware topic then a patching topic.
Both the BCR and the Axoloti are quite flexible in connecting through midi. So it is not possible to find one patch "that controls them all". A possible workflow could be:
Design or pick your patch on the Axoloti. Decide which elements you want to be controlled through midi. Assign midi cc numbers to the controls in your patch. There are several ways to do that. You can find them on the forum.
Next you create a patch on the BCR. This can be done by using the controls on the BCR or by using an auditor like
Another option would be to assign " standard" CC's in your BCR and assign those to you Axoloti patch as you need them. But the BCR gives you a lot of options like min max type of ring display. You will not be able to use that.
So like a lot of things in the "flexible" world there is no quick fix. You have to put some work into it. But hey ... that is where the fun is.