If your host listens on all interfaces for SMTP connections on the SMTP port, then I think you should be able to use the docker default network as all containers are connected to thatand it has the host as gateway. So, configure that as SMTP host and see if any emails are logged by your host email server.
[root@bitwarden ~]# docker network inspect docker_default
[
{
"Name": "docker_default",
"Id": "5fafb2d2f5a54dde20c82efa23286bf15279052e416bd8dc8fda45bdfff15cdd",
"Created": "2019-05-04T14:09:14.599099535+02:00",
"Scope": "local",
"Driver": "bridge",
"EnableIPv6": false,
"IPAM": {
"Driver": "default",
"Options": null,
"Config": [
{
"Subnet": "172.21.0.0/16",
"Gateway": "172.21.0.1"
}
]
},
"Internal": false,
"Attachable": true,
"Ingress": false,
"ConfigFrom": {
"Network": ""
},
"ConfigOnly": false,
"Containers": {
"069b80e1d32c77c2d6ba0c7aab78e57bfdfc6f3d7c0d0f0c1c1a788f874caadc": {
"Name": "bitwarden-api",
"EndpointID": "1c9e63277f4c0019d7b6555cb93d712aa34a12e7a9955cc4c37c7fd6f2ba39a5",
"MacAddress": "02:42:ac:15:00:04",
"IPv4Address": "172.21.0.4/16",
"IPv6Address": ""
},
"32a41e3daa82bec8fa048345b386e5e2f0b311aae1476b678529afe19c328d4b": {
"Name": "bitwarden-web",
"EndpointID": "a8b6a5850e577b1505a5b5c669d1bc770d78952705f76a98cf22720bf6be2844",
"MacAddress": "02:42:ac:15:00:06",
"IPv4Address": "172.21.0.6/16",
"IPv6Address": ""
},
"3e35b4a3b87e5ef50e81f99f66e3b1373ba1fddf064d1eee319b54b7b91f74f5": {
"Name": "bitwarden-attachments",
"EndpointID": "ba25cb4ac5be94ca4ea7a0fde51f1500bc049f05aac2e25d54da8995748ec5e7",
"MacAddress": "02:42:ac:15:00:02",
"IPv4Address": "172.21.0.2/16",
"IPv6Address": ""
},
"4d4594513b957e07f39ea38146ef5c376d55c749cd1fe58d5da3271f9c939d72": {
"Name": "bitwarden-icons",
"EndpointID": "fd1e44bc660e7abc97d5bf1111218748b938cd3172d92e3bcd63900f295f62e2",
"MacAddress": "02:42:ac:15:00:03",
"IPv4Address": "172.21.0.3/16",
"IPv6Address": ""
},
"583448ef1b01095086918672a52e106ecd96cb634ca3e199e6b599bc81246925": {
"Name": "bitwarden-nginx",
"EndpointID": "71a999881d2ddf8e7cfea8737dbfcb4a43fd371380e18b5f231b03f53a96e305",
"MacAddress": "02:42:ac:15:00:0a",
"IPv4Address": "172.21.0.10/16",
"IPv6Address": ""
},
"61b588cbe5e23d5362f851b391f0fab9f2681a4d6165d04007e99f395d120424": {
"Name": "bitwarden-mssql",
"EndpointID": "0c16ef4bf9ab66aef5f6fadbdbce990925e7cb5795a11143e4815f620e765c1b",
"MacAddress": "02:42:ac:15:00:09",
"IPv4Address": "172.21.0.9/16",
"IPv6Address": ""
},
"69995ab45c119a1e4202ea64c2fbcd554e0e8e519e853957ea71e38c53e95b20": {
"Name": "bitwarden-identity",
"EndpointID": "f8d070d90146db3ed97f99e9ddf59a03b3a7b09a66a099965673e7601408ea1b",
"MacAddress": "02:42:ac:15:00:07",
"IPv4Address": "172.21.0.7/16",
"IPv6Address": ""
},
"809809950b35c123355d34cd3c55357ec010d187b17b3682b3ccd840ecc57ade": {
"Name": "bitwarden-notifications",
"EndpointID": "79a1b57d8860c47578acd4498573a0109793e05d354e6a6836d074c6f5e92403",
"MacAddress": "02:42:ac:15:00:05",
"IPv4Address": "172.21.0.5/16",
"IPv6Address": ""
},
"c0b90132a1d8749894b487c6eed3c9e69320777645935cff28d1f85cceee34f1": {
"Name": "bitwarden-admin",
"EndpointID": "d564c4978dabfb0d09a2ce0a0cc576321cd5a334c782707c460eed94ca915c9e",
"MacAddress": "02:42:ac:15:00:08",
"IPv4Address": "172.21.0.8/16",
"IPv6Address": ""
}
},
"Options": {},
"Labels": {
"com.docker.compose.network": "default",
"com.docker.compose.project": "docker",
"com.docker.compose.version": "1.24.0"
}
}
]
[root@bitwarden ~]#