That's true, because both my guitar and bass guitar use 1/4" jacks, but my main concern was whether the speaker itself on the guitar amp would vibrate itself apart because of the low frequencies of the bass guitar. I've seen vids on youtube of guitar amplifier speakers that destroy themselves when they are played through with a bass guitar.
That's a legitimate concern, especially with the tiny 8" driver that the Mustang combo amp uses. As Mayhem said, start with the volume set low, and ease it up gradually.
Traditional guitar amps, especially the vacuum tube (thermionic valve) types don't have very good bass response to begin with, and the drivers in guitar combo amps, which are often open back designs, use low compliance drivers to prevent over-excursion of the driver voice coil. Nevertheless you can overextend the driver if you try hard enough. If you do, you'll know; it makes a surprisingly loud "crack" when the voice coil bottoms out. As soon as you hear a crack sound, turn the volume down!
You said that you want to get some distortion out of the amp. You can do this by keeping the "Volume" and "Master" knobs set low (keep the "Bass" knob right in the middle) and use the "Gain" knob to overdrive the front end.
Because the signal coming out of the average electric guitar or bass is made solely by the vibration of the strings, guitar (and bass) amps have two gain stages: one to bring the voltage up to line level, and another to drive the speakers. When you have an amp with separate controls for each gain stage, you can crank up the first stage to produce distortion without overloading the power stage or the speaker driver(s).
Some guitar players prefer to overdrive the high power stage, which is fine as long as the drivers can handle it. The most popular "4x12" guitar cabinets have four 12"
Celestion drivers in a closed-back cabinet, and can handle the full output of a "100W" guitar amp at full tilt. Since you're using a bass with a guitar amp combo, you will
not want to get your distortion by overdriving the power section and/or the speaker cone!
I don't know precisely how the headphone output on your Mustang amp, but if it's enough to drive headphones, it will totally overload your bass amp's instrument input stage. This may or may not give you the sound that you desire. If you want to use the effects on the Mustang amp without overloading the bass amp's front end, you'll need an attenuator of some sort to lower the signal level down from line level down to the instrument level that the bass amp expects. You might be able to do this by keeping your "Volume" and/or "Master" knobs set low. An external box like the
Electro-Harmonix Signal Pad (~$50US) might be a good idea. And of course you'll need an adapter cable to connect the tiny TRS male headphone jack to the 1/4" TS male input on your bass amp.
