I believe the Fender Bassman is usually sought by guitarists, although its original purpose was as a bass amp.
Fender Bassman amps have a "Bass Instrument Input" and a "Normal Instrument Input." (Normal on right in photo.)

They aren't strictly bass amps.
As for just running a guitar through a pure bass amp being bad for it, not so. You will sound like ass, because bass amps are built to deal with the normal ranges of and produce the best sound for...you guessed it, bass guitars. So you will have to do some uber EQing to get those top-end notes heard, because a bass' range is so much lower than a guitar's.
Therein can lie the suspicion that it can be bad for the amp. If you're just using the amp's EQ, you're fine. But sometimes if you're running things like high-gain distortion pedals or EQ pedals to boost your top end, it can feel like you're telling the amp to do something it is not made to do, which is bad for it. It isn't usually, but just pay attention to it, and if it starts making weird noises, stop using it.
However, running a bass into a guitar amp is a bad idea. Basses have a higher output than guitars, which can drive the amp very hard, and then adding the extreme amounts of bass frequencies being shoved into the guitar can do no small amount of harm to the amp. Be careful!
Actually, my old band's bassist used a guitar amp with his bass to get this distorted bass sound not unlike a dog barking. Sounded awesome until the amp got fried and stopped working
Case in point. The distorted bass sound was the amp saying "STOP DOING THAT TO ME YOU BLOODY STUPID BASSIST." The reason it sounded like a dog barking and not a normal bass was the amp was being driven so hard that it didn't come out as distortion like a normal hard-driven amp, but rather it was driving it so hard that it was actually destroying the amp bit by bit.