| Yes, a PA is very broad-ranged. It's designed to handle everything, which is why so many people run bass through it instead of through their own amp.
I'm going to assume the least knowledge to help explain this to you. With a regular bass and bass amp, here's how it works. The bass plugs into the preamp, which creates a sweet-sounding tone (hopefully), which then goes into the power amp, which then makes it loud, and finally the power amp send the signal to the speaker. The bass amp head contains both the preamp and the power amp.
The PA works the same way. Signals go into the mixing board (like a preamp) where there are mixed and equalized, then sent to the power amp, and then to the speakers.
So you can run the bass directly into the mixing board, but it's not designed to make bass tones sound sweet, so it won't sound as good as a bass amp. What many people do is use a bass-specific preamp/direct-in box (kind of like a pedal) between the bass and the board to get the sound they want. You can also run the signal from your bass amp's preamp to the board. Some amps have direct-out jacks just for this, other times you run the plug from the effects send jack. Don't plug the output of your power amp into the input of the mixing board, it will cause damage.
The PA has a power amp that's only 40 watts? That seems really small. Unless the PA has over 150 watts, you definitely need to bring your own amp. Maybe your church has great acoustics and you want quiet music though, so I can't say for sure. | 
