Bahadur resembles bagatur which is one of the well known Bulgarian titles (sometimes written as bogotor) and in Russian is transformed into bogatir. It's not originally Turkic but a loanword like many other Turkic words.
The Persian form of this name "BAHADUR" is one of the oldest names in the Turkic language. Its original form is "BAGATUR" and means "brave, warrior, bold, hero". Although classified as Turkish name, it was widely used in Mongolic language; this makes researchers think it has a Turkic-Mongolic common origin. This name was also picked by khagans and kings, i.e. Asian Hun Emperor MO-TUN (BAHADUR II), last Indian ruler before the English invasion. This name was first used in Persia during the Turkish dynasties ruling Persia (Seljuks, Sasanies, Karahanlis etc.) In the Ottoman Empire era this name passed to Anatolian Turkish from Persian and began to be used in the Persian form "Bahadir". Today it is a very popular masculine name in Turkey.To sum up, this name's transfer occurs as Turkic(Mongolian) to Persian and then to Turkish once again.