Can I Connect Mini to Bolt Directly with Ethernet Cable?

Technically, yes, with an Ethernet Cross-over cable.
But without the benefit of a router, you'll have to set everything up manually. Plus how will you provide internet access to both TiVos?

 

Your Mini still needs to access TiVo's mother-ship for TV Guide and Subscription Status via Internet; I'm assuming, right now that happens via MOCA to Bolt with Bolt being connected to some sort of router with internet access. An Ethernet cable to the router will provide an alternate route to Bolt and Internet.

 

How is your bolt getting internet access? Via coax (MoCA)? If yes, the Bolt ethernet port should provide internet to any ethernet device.

My set up is coax from MoCA adapter (FiOS G1100 router) to Roamio Plus (set as MoCA Bridge [MoCA + Ethernet]) and coax (MoCA) to Mini. In addition, I have my Fire TV connected to the Roamio Plus ethernet port for internet access.

So, you should be able to disconnect the coax from the Mini and connect Bolt ethernet to Mini ethernet. With this setup, Network Settings on the Bolt should be:

Ethernet: On
Wi-Fi: Off
MoCA: On

 

Yes, with the BOLT configured as a MoCA client, you can leverage its built-in MoCA bridging and its otherwise unused Ethernet port to extend the home network to other Ethernet-capable devices, such as the Mini.

That said, it might be worthwhile looking into what ails the MoCA network. (A good start is a diagram, however rough, of how all the devices interconnect.)

 

If you can run an Ethernet cable through the wall to the Bolt just use a 5 port Ethernet switch and it'll work. Plug the Ethernet cable from the router, an Ethernet cable from the Bolt and the Ethernet cable from the Mini all into the switch. This one for $8 delivered will do nicely: Amazon.com: Online Shopping for Electronics, Apparel, Computers, Books, DVDs & more