Basically I'm writing a bash script that is supposed to select multiple values from 2 mysql tables.
mysql -h "mydomain.de" "database1" << EOF
SELECT serverId FROM member WHERE username = @user;
SELECT slots FROM server WHERE id = @serverId;
In your case, you could just do it in one SQL SELECT:
#!/bin/bash user="testuser" slots=$(mysql -uuser -ppassword -Ddatabase -N -e "SELECT slots FROM server,member WHERE server.id=member.serverId AND member.username=$user;")
You might want to play with bash arrays to parse results.
If that's true you can make multiple mysql-client calls to do that, keep in mind it's always better to make your DBMS perform the joining/sorting/formatting instead of your own code.