Automatically write new bash history to change-log file
Try using GNU Screen or Tmux. These are called "screen multiplexers" but you'd get a number of benefits


The commands you run will continue running even if you disconnect, or you have network related connection drops. Both software allow "re-attaching" to the running session
Command outputs will persist in memory. You can start a long running command, log off, then connect back some time later and see the output of the command.
Save the whole shell session to a file. You can have the log of all the commands you issued, as well as the output you got, in plain text format.