Relay not outputting voltage
If you are hearing the relay clicking when expected, then you are probably driving it correctly.  The problem is therefore on the relay output side.

Check the relay contacts with a ohmmeter.  You have 3 contacts, which should be labeled something like NO (normally open), COM (common), and NC (normally closed).  The relay switches COM to one of NO or NC.  When the relay is unpowered, COM is connected to NC, and NO is open.  When powered, COM is connected to NO and NC is open.  This is easy to verify with a ohmmeter.

If the relay is working according to the ohmmeter test, then you have its outputs connected wrong.  Since you have given no real information about your system on the output side of the relay, there is little more we can say about it.

Note that relays don't "output voltage".  If you are expecting this bubble machine thing to somehow be powered by just connecting it to the relay without a power connection, then you need to go back and learn some very basic concepts.