Note:
Last in the post you'll find the cheapest, lightest but at the same time pretty solid sounding solution I have. What I currently use myself as practice setup:
A small old sound interface run in direct monitor mode powered with a wall power outlet USB adapter, then with the bass plugged into the HI-Z preamp input and a pair of headphones in the Headphones output.
Know it's well over 50$, almost 100$ over and it's only a head that also would need a cabinet in addition.
But this is pretty cool:
Hotone Nano Legacy Thunder Bass 5-watt Micro Bass Head
Then of course there's the option of getting a cheap preamp too with headphones output.
Headphones output would allow you to basically hook up any small or bigger active speaker unit to it, as for instance computer speakers.
Know you don't live in Europe, but this is amazingly cheap concidering the features, and according to someone here on Talk Bass who tried it it should sound pretty good as well and work well:
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Just slightly over 110$, which though still would be over your budget.
Gonna be hard to find something useful at under 50$, so
maybe you should think about what you already have at your disposal that could possibly be used as an alternative practice amp, like an
old Hi-FI amplifier or similar.
What I personally have used in the past was the
AUX input channel on an old living room organ, which amp and speakers actually both sounded and handled bass really well.
I am not familiar with how it works in USA, but actually here in Denmark these old organs are often put up all for free if you come to collect it yourself, and if you know anything about electronics it should be possible to extract the actual amp so you don't have to drag around with a colossus organ.
Right now what I use for practice when I need more than practicing on my electric bass just acoustically is an
old M-Audio Fast Track
sound interface which I
power though the USB connection with a USB power adapter for wall outlets and further more place a Behringer Ultragain Mic100 dead cheap microphone preamp in front (modded with a new EHX preamp tube instead of the cheap Chinese one it came with), which strictly isn't necessary since the sound interface already got an instrument high impedance input with a preamp.
Then I just put it in direct monitoring mode and plug my headphones into the Headphones output of the sound interface and am ready to go.
Actually sound pretty good, and again you could connect any active speaker unit either via the Headphones output on the interface or the stereo phone line out plugs on the back of it.
If you don't already got an old USB powered sound interface, it should be possible to find one cheap, and even if not strictly necessary to use it the microphone amp does make it sound better, but that ought to be able to find used dead cheap as well.
So this is basically my practice "rig":