I think Dota doesn’t run on proton, i had no problems running the native linux version with my laptop intel i7 + nvidia 1050ti, but it was on X11, u can probably choose that on login screen.
What i think you need from a fresh install (i don’t remember exactly what i did at the time):
enable multilib
install nvidia package or nvidia-lts depending on which kernel you’re using, or nvidia-dkms plus headers of your kernel
install nvidia-settings nvidia-utils lib32-nvidia-utils nvidia-prime (never used bumblebee i just use prime-run)
install steam or steam-native-runtime
install game on steam, change launch command to prime-run %command%