1. Disable iptables

$ sudo vim /etc/docker/daemon.json

{
  "iptables": false
}

2. You have to set Docker's bridge postrouting in ufw:

$ ifconfig docker0

It should returns something like this:

docker0: flags=4099<UP,BROADCAST,MULTICAST>  mtu 1500
        inet 172.17.0.1  netmask 255.255.0.0  broadcast 172.17.255.255

So docker0's network is 172.17.0.1/16

sudo vim /etc/ufw/after.rules

*nat
:POSTROUTING ACCEPT [0:0]
-A POSTROUTING -s 172.17.0.1/16 -o eth0 -j MASQUERADE
COMMIT

3. Finally you have to restart UFW and Docker

sudo ufw disable
sudo ufw enable
sudo systemctl restart docker

4. Also, ufw will keep blocking unless you allow forwarding

sudo sed -i -e 's/DEFAULT_FORWARD_POLICY="DROP"/DEFAULT_FORWARD_POLICY="ACCEPT"/g' /etc/default/ufw
sudo ufw reload