A friend and I made a few changes to make this mod work for us on 1.1 as it was the last mod we still needed for our multiplayer save.
You can download our zip from https://drive.google.com/file/d/1h3I_AsDqsBAdqguxexSJ8q24Sexa4Z2e/view?usp=sharing
Just drag the zip into the appdata/roaming/factorio/mods folder and it should be selectable in game.
Alternatively, if you don't trust a random person on the internet to send you a zip file, here are the changes we made:
Zip file and first folder inside: changed name to BetterBots_1.3.8
control.lua Line 6 changed from: require 'mod-gui' to: local mod_gui = require("mod-gui")
scheduler.lua Line 1 changed from: require 'mod-gui' to: local mod_gui = require("mod-gui")
info.json Line 4 changed version to "1.3.8"
info.json Line 9 changed factorio_version to "1.1"
Note: We have not tested wired roboports, roboport power field, and roboport sensor array functionality as we don't use those in our base