Bela expects to find a DHCP server at the other end of the ethernet cable. If you plug your computer in there, by default the computer will expect the same. So with the two devices expecting to be assigned an IP address by the other, nothing good will happen.
Are you 100% you are sharing it with the correct interface (i.e.: your ethernet interface)? In this case the computer should start acting as a DHCP server and Bela should be happy and bela.local
should start to work.
Worst case scenario, you'd need to change the setting on Bela so that it has a static (self-assigned) IP address on the ethernet port. Then you could set a static one on your computer, too, and - as long as they are "compatible" - everything should work. In order to do this, you could plug that ethernet cable from Bela into a home router, which will give it an IP address, and you should be able to find bela.local
by connecting over wifi to the same router. I can then tell you how to change the setting on Bela so that it uses a static IP on the ethernet port.