Based on the designs of the vehicles, Bravado is most likely based on Dodge, even though the Rumpo and the Paradise are based on Chevrolet vehicles, and the Feroci is based on a Lexus vehicle, while the new vehicle, the Verlierer, is based on a TVR. Also, Bravado's logo of a charging bull is a parody of Dodge's ram logo used since 1993. In Grand Theft Auto V they have a TV commercial showcasing the Bison, Gauntlet, and Buffalo, parodying various Dodge commercials.
In real life, Bravado is a company that manufactures bras for pregnant women. This may be a play on the fact that the real-life counterpart of the Bravado, Dodge has a badge that is considered by some to resemble a diagram of the female reproductive system, when in fact it is the head of a ram.
The bull's mouth of the Bravado logo will look like a glans penis (male sexual organ) when observed closely.
Bravado seems to play on its car names relating to the ram on its logo, with names such as Buffalo and Bison (both four-legged mammals sporting horns).
Besides its logo and its models being represented by animals relating to the cattle family, it's a reference to Taurus being the astrological/astronomical sign after Aries (is represented by a member of the sheep family while Taurus is represented by a member of the cattle family).
Bravado is defined as "a bold manner or a show of boldness intended to impress or intimidate."
By 2013, it appears that Bravado neared bankruptcy at one point, and was bailed out by the U.S. government using taxpayer money. This parodies the actual bailout of the auto industry in 2008.