see : https://github.com/influxdata/influxdb-docker/issues/14

docker_compose_possible_fragment1.yml

    influx:
        build: ./docker/influxdb
        environment:
            ADMIN_PASSWORD: 'blabla'
            DATABASE_NAME: 'testdb'
            USERNAME: 'simpleuser'
            PASSWORD: 'securepass'
            INFLUXDB_HTTP_AUTH_ENABLED: 'true'

docker_compose_possible_fragment2.yml

    influx:
        build: ./docker/influxdb
        environment:
            ADMIN_PASSWORD: 'blabla'
            DATABASE_NAME: 'testdb'
            INFLUXDB_HTTP_AUTH_ENABLED: 'true'

Dockerfile

FROM influxdb:0.13

ADD setup_and_start.sh /root/setup_and_start.sh
RUN chmod u+x /root/setup_and_start.sh


ENTRYPOINT /root/setup_and_start.sh

setup_and_start.sh

#!/usr/bin/env bash

set -m

INFLUX_HOST="localhost"
INFLUX_API_PORT="8086"
API_URL="http://${INFLUX_HOST}:${INFLUX_API_PORT}"

wait_for_start_of_influxdb(){
    #wait for the startup of influxdb
    RET=1
    while [[ RET -ne 0 ]]; do
        echo "=> Waiting for confirmation of InfluxDB service startup ..."
        sleep 3
        curl -k ${API_URL}/ping 2> /dev/null
        RET=$?
    done
}

if [ ! -f "/var/lib/influxdb/.init_script_executed" ] && [ -n "$ADMIN_PASSWORD" ]; then

    echo "=> Init script : starting InfluxDB in background ..."

    BACKUP_INFLUXDB_HTTP_AUTH_ENABLED=$INFLUXDB_HTTP_AUTH_ENABLED
    INFLUXDB_HTTP_AUTH_ENABLED=false

    exec influxd   &

    wait_for_start_of_influxdb

    influx -execute "CREATE USER admin WITH PASSWORD '${ADMIN_PASSWORD}' WITH ALL PRIVILEGES;"

    if [ -n "$USERNAME" ] && [ -n "$PASSWORD" ]; then
        influx -execute "CREATE USER ${USERNAME} WITH PASSWORD '${PASSWORD}';"
    fi;

    if [ -n "$DATABASE_NAME" ] && [ -n "$ADMIN_PASSWORD" ]; then
        influx -execute "CREATE DATABASE ${DATABASE_NAME};"
    fi

    if [ -n "$DATABASE_NAME" ] && [ -n "$USERNAME" ]; then
        influx -execute "GRANT ALL on ${DATABASE_NAME} to ${USERNAME};"
    fi;

    INFLUXDB_HTTP_AUTH_ENABLED=$BACKUP_INFLUXDB_HTTP_AUTH_ENABLED

    touch "/var/lib/influxdb/.init_script_executed"

    if ! kill -s TERM %1 || ! wait %1; then
        echo >&2 'InfluxDB init process failed.'
        exit 1
    fi
fi

echo "=> Starting InfluxDB in foreground ..."

#if [ "${1:0:1}" = '-' ]; then
#    set -- influxd "$@"
#fi

# exec $@

exec "influxd"