First of all you need to understand that while you can get good sounding GUITAR amps for bedroom use, that's not really gonna happen with bass amps. "Bedroom size" bass amps won't sound great, period. Any bass amps that DO sound great will also be WAY overkill for bedroom use and be audible in the entire building. For bedroom practice I would recommend some kind of modelling gear with a headphone output and a good pair of headphones.
As for the choice of bass.... A Squier Classic Vibe J or P is a good, safe choice. They're easily as good as MIM Fenders, if not better. The lower end Squiers (Sonic/Affinity) aren't nearly as good though. The Sonic series in particular feels extremely cheap IMO. In that price range you can get far better basses from the likes of Harley Benton.
But... with the bands you refer to, maybe you would be happier with an active, more metal/progmetal-oriented bass? Something like an Ibanez SR300 might be a good choice if you're on a tight budget (and actually quite decent basses regardless of price). I normally never recommend active basses to beginners though, for mainly two reasons:
1) With an active bass it's much easier to dial in a poor tone if you don't know what you're doing. Boosting the lows too much is perhaps the most common mistake. As a guitar player you're probably used to dialling in a great tone alone, and then still have a great tone when playing with a full band. That's not gonna work with bass. With bass it's nearly always (unless you're a virtuoso soloist) all about how the bass SITS IN THE MIX. The best tone for bass with a band is almost never the tone that sounds the most impressive when playing alone. With a passive bass it's actually hard to dial in a tone that doesn't work reasonably well in the mix. With an active bass it's VERY easy to dial in a tone where the bass will end up boomy, muddy and get completely lost in the mix.
2) The electronics in passive basses can usually be very easily repaired, relatively cheap. The electronics in active basses is a different story. If the active preamp fails you could end up with a rather expensive repair. If you buy active, at least buy a NEW one from a store with a good warranty policy.
I'm not saying you shouldn't get an active bass. Active basses are great (although I personally prefer passive). You also have experience as a guitar player so I'm assuming you're not a total beginner. But these are still things you need to consider before making a decision.
And as always: The best investment you can EVER make when buying basses in the low-to-mid price range is to factor in the cost of a professional setup, including levelling/crowning the frets if needed (and it very often is on brand new instruments, even on expensive MIA Fenders).