No problem to enable MP3 and Video Player functions in a US/EU firmware 3590 and store files on the unit: [Only registered and activated users can see links. ].
However, i don't think the 3590's BT will link to any BT enabled car stereo/infotainment unit only to BT phones so you'd be stuck playing thru the powered mount's single speaker. Neither the MacIntosh or Pioneer units in my two cars won't BT hook up like that anyway to any BT nuvi. For playing music files like that you'd need an FM transmitter present in the nuvi of the type in older units such as nuvi 6x0/7xx and the hardware's not present in any 3x9x. Maybe easier to just buy a ciggy-socket FM Transmitter for a few euros from China and use that as i did with my old Pioneer, or if your head unit plays MP3s on a CD/DVD or has USB-in, A/V-in or ipod connectivity do any of those ways.