It's not bridge street. There's a community group called 'The Bridge' who operate out of a building near BACA school, and there's a large car park there the club uses, so it's referred to as the bridge car park.
It's Lucraft Road BN2 4PN...
Here's a pdf about travel options
http://www.seagulls.co.uk/documents/travel-guide-april14229-1169722.pdf
Parking is priced at £13 if booked at least 3 days in advance, otherwise it is £15.
There are parking restrictions around the stadium in residential areas. That means the closest free on street parking would still require getting a bus, or a 25min walk.
If I remember rightly, you are Finnish, so I would presume are thinking about visiting. If you are staying in Brighton...