Well, think about the mods done to the Bassman to be more guitar-friendly...
You might have made coupling caps, cathode bypass caps and/or tone circuit caps smaller to push them into the higher guitar range or to strip out bass to keep things from getting really muddy when you have a lot of distortion. So sometimes bigger caps are used.
You might use larger diameter speakers in a bass setup (think Ampeg B-15), but then again you might use small speakers for a punchy sound (think Ampeg SVT 8x10 cabinet, or an Eden 4x10 cabinet).
A guitar amp might use an under-rated speaker, whose power handling just equals the amp's output power, so that you can be assured of driving then speaker until the cone physically twists and bends during a note, giving you "speaker distortion". That's not to rough on the speaker unless you play full-power square waves by blasting the amp with a RAT pedal in front of it. Square waves heat the speaker more than sine waves of the same peak voltage, and can burn up a speaker. But you likely also know if you play cleanly through a guitar amp, the speakers generally last forever.
Well, in a bass amp, you almost always play cleanly. But those low notes make the cone jump really far. The bass' notes are down around the bass resonant frequency of the speaker, and make it jump so far forward and back on the initial transient that the speaker literally tries to pull itself apart. So part of the genius of the 10" speaker in the bass cabs is to have the resonant frequency a little higher so the cone doesn't jump through the grill cloth, while at the same time you use much more speaker power capability than amp-power capability. Yes, you don't get the gut-wrenching low end that a 18" or 15" speaker will give, but the roll-off of the lowest tones gives the bass a punchier, more authoritative sound that really jumps through a mix.
And there's a psychoacoustic effect where if you hear all the harmonics of a note, even if the fundamental is missing, your brain fills it in as though it were there. So you feel as though you're hearing all that low end even though you're not. Just recall all the recorded music where the lows of a kick drum are rolled off, but you still know you're hearing a kick drum.
But in the end, you're gonna be in a teaching situation, playing fairly soft. I'd use at least a 30-50w guitar amp with a lot of speaker cab, if in a setting where the amp can be left in place all the time. You won't have to worry about speakers blowing out with the amp set on 2-3, and the sound will be plenty clean. You might prefer keeping the treble knob rolled back a bit, or viewing it as a presence knob, while adjusting the mid knob for the high end of the bass notes. Should work out fine.