Bandwidth of an antenna is primarily dependent on the design of the antenna and the electrical radius of the active element(s).
With FM radio stations, the high power 1 - 100+ kilowatt transmitters, allows a lot of loss with respect to the receive antennas: any approximately eighth wavelength wire or longer will adequately receive any station in range(20 to 150 miles depending on terrain and antenna gain or loss).
Most car antennas are given a length the corresponds close to the center of the FM band. The power output of the stations make up the difference.
In the AM band the output power tends to be lower overall( .01 - 5KW+), since the band will travel longer distances. AM Reception is done in car radios through the use of loading coils applied to the FM antenna. The efficiency of the antenna + loading coils is about 5 to 60 percent of the power available in the airwaves. Reception depends on propagation factors.
Bluetooth is a whole different story, it operates on the 2.4 GHZ spectrum with a power in the milliwatt power range. To minimize interference with WiFi occupying the same bands, it produces a signal that hops through all of the allocated frequencies in such a way to cause the minimal amount of disruption to the WiFi channels it conflicts with.
Now back to antenna bandwidth:
There are very wide designs based on angles like the rhombic design (high gain, highly directional, 1+ decade of 3db bandwidth)
The length specified wideband: (each band must be represented as a length in the elements of the design)
log-periodic(Medium gain and directional)
I would be failing to represent all widebands, I am sure I skipped many, if I did not include the End-Fed-Half-Wave(EFWH). The high impedance of an EFWH makes it a perfect longwire antenna for evenly divisible frequencies.
Back to the electrical radius(where surface area dominates):
The bowtie UHF, similar in concept to VHF rabbit ears:
Four, or two, short sticks emanating from a common point and spaced appropriately.
The bounding frequencies of this design are dependent on the length and size of the elements.
For a dipole, the bandwidth is most dependent on the size of the conductor, but may be extended by introducing a second(or more wires) of the same length using (relative to wavelength) small spacers.
For microwave frequencies like 2.4GHz when space is a consideration, microstrip fractals tend to replace conventional antennas. The fractals offer a wider bandwidth and more electrical length, therefore more bandwidth for a smaller design.
Maximizing surface area leads to a higher bandwidth antenna.