Why doesn't the tone control work for the bridge-only pickup selection on a Stratocaster?
On the majority of Stratocaster guitars whether made by Fender or by Squier, when you select the bridge pickup alone, neither of the tone controls affect the sound. The bridge pickup is "always on 10" no matter what you do with either tone knob. However the tone controls do work for the other four switch positions.
Does this mean your Stratocaster guitar is defective?
It was designed that way by Mr. Fender himself, as in Leo Fender, the guy whom Fender guitars are named after.
What Leo wanted with the Stratocaster is a pickup position that sounded similar to a steel guitar; something that really, really stood out with a somewhat piercing and shrill sound (typical for pedal steel guitars of the time). Thus, the bridge pickup selection has no tone control wired to it whatsoever.
Do all Strats have no tone control for the bridge-alone selection?
No. There have been several models of Stratocasters over the years that do in fact use the Tone 2 knob (the one near the bottom of the guitar) to affect the bridge-only pickup selection. For example, several American Strats in the 1990s featured what were called TBX tone controls, and many that were delivered with TBX (if not all of them) did have tone control for the bridge-only pickup setting.
Do you need TBX for bridge-alone tone control? No. All it takes to get tone control on the bridge-alone setting it to solder a very small wire between two terminals.
This is a Strat's 5-way switch:
In the photo above, you see four terminals on top and four on the bottom (one is hidden from view on the bottom, but trust me, it's there).
In a diagram view, the terminals look like this (and I have one part circled for a reason):
One side of the switch is wired to connect the pickups. The other side connects your master volume and two tone controls (blue is Tone 1 above and red is Tone 2).
The circled part you see above is what you'd need to connect if you want Tone 2 to also control the bridge-alone pickup tone setting. When you take apart your Strat and look at the switch, you'll see this in plain sight. Simply solder a little wire between the Tone 2 terminal and that open terminal, and ta-da, you've got tone control for the bridge-alone pickup selection.
If when you take apart your Strat you're confused as to which terminals to connect together with that small wire, just follow the wire from the Tone 2 pot to the switch. Wherever it connects, you know you've got the "correct side" of the switch and know where to solder in that the small wire.
If all of this sounds too scary to do on your own, every good guitar tech knows how to do this ridiculously simple modification. In other words, yes you can afford to pay a tech to do this because it hardly takes any time or effort to do.