Is it a two channel amp that is bridged, or a one channel amp?
If a one channel then no you should not hook up the other sub, you would have to do it in series and would lose the "kick".
If a two channel amp then yes, remove the bridge and run one sub on each channel.
A speaker doesn't "draw power" from an amp, the amp powers the speaker, so the bigger concern would be to hook up a speaker rated at 150watts to a 300watt amp.
But the amp is effected by the impedance of the speaker, 0 ohms is a dead short which will burn out the transformer on an amp.
Speakers are usually 8 ohms and on a heavy bass note might drop to 6ohms
Subs are often 4 ohms and will drop to 2 ohms when thumping, lol.
So they get close to shorting.
But here is the conundrum, the closer you get to 0 ohms the more power you get, i.e. 0 resistance = FULL POWER, which is why subs are often 4 ohms.
Hooking up multiple speakers
If you hook up two 8 ohm speakers to one amp(one channel) and use + and + on one terminal and - and - on the other terminal this is call parallel wiring.
But what you get and what the amp sees is 8ohm + 8ohm = 4ohms
If this amp is rated for 6-8ohms then if you ever turn it up it will probably fail.
If it is a amp rated for 4ohms then that will be fine.
If you wire two 8ohm speakers like this:
This is called series wired and amp sees 16ohms, which would not cause an issue BUT OHMs are power, so you basically have cut a 200watt at 8ohm amp down to 100watts.
The new Digital amps often don't like any ohms out of their range so 16ohms could cause them to fail over time.
And series wiring shouldn't be used if you have two or three way speakers, these have built in crossovers which would not play well together, won't hurt anything just less sound quality.
So paralleling two 4ohm subs would get you ..........2 ohms at the amp, big bass note hits and........0ohms DEAD SHORT you lose, lol.