Just my opinion, but this thread is very difficult to follow because though individual questions are being answered, the answers must be taken in context. The initial question was simply whether a particular surface-mount bridge-rectifier was suitable for LED passenger car lighting. Then the discussion meanders to regulators, adjust-ability, extended operation (presumably flicker suppression), and so on.
To put things in context, here's GRJ's LED module in the center. The point is this is an engineered-design meaning the components were selected to operate together with specifications commensurate to the application.
One side discussion was on the use of larger bridge rectifiers. Well, take a look at the variation in sizes as you go from the surface-mount bridge on GRJ's module, to a 1 Amp bridge (what OP initially inquired about), to a higher Amp bridge as suggested by others.
Then the capacitor. Take a look at the size difference between the 330uF surface mount cap on the module vs. 470uF and 1000uF caps one might buy if components are acquired one-at-a-time.
Then the DCS inductor. Take a look at the tiny surface-mount 22uH inductor on the module vs. a 1/2W part you might buy if acquired one-at-a-time.
Then the idea of a resistor plus a potentiometer for brightness adjustment. Compare the resistor and potentiometer on the module to a 1K 1/2W resistor as suggested and the 10k potentiometer most recently brought up from Amazon.
Then the regulator. The LED module uses a LM317 IC. A DC-to-DC module from eBay is many times larger though can handle much more power. But is this power needed to light a passenger car? (Answer: No. But the module is inexpensive and simple to hook up). The low-power AC-to-DC converter board discussed earlier also has all the components (including a regulator IC) but is more suited to powering a few LEDs rather than a full-length passenger car LED strip.
I find a regulator isn't especially useful or much of an advantage.
The regulator has the advantage of maintaining constant brightness for intermittent track-voltage loss due to dirty-track, going over a switch, and so on. If you only have a capacitor, as soon as track-voltage is lost, the capacitor voltage immediately starts dropping as it supplies current to keep the LEDs going. This voltage drop appears as a drop in brightness.
If you have a regulator IC, the LED brightness is maintained even as the capacitor voltage drops. This gives superior flicker reduction. To be sure, that's simply my opinion and what's good-enough is a to-each-his-own, your-mileage-may-vary. But since an LM317 regulator IC is less than 15 cents, it's something to consider.
As GRJ mentions, if you use a voltage/current regulator IC like the LM317, in general you can use lower-power resistors and potentiometers. Note the difference in sizes between the surface mount resistor+potentiometer as used on the LED module vs. "loose" components as were suggested in other posts.