The chairman hopes to see a big turnout at the WFA Cup final as the Seagulls take on newly-crowned league champions Manchester City.
Albion will start as underdogs on Sunday (3pm).
But they upset the odds to win at Arsenal in the quarter-finals and came back from 2-0 down at Liverpool in the semis.
They then sparked a City celebration by securing them the league title when a much-changed Seagulls side drew with Arsenal.
Albion have been building their away following this season, which remains a work in progress although progress and numbers have been encouraging.
Bloom hopes as many fans as possible get to Wembley.
He said via the club’s social platforms: “Brighton fans, we are heading to Wembley for the FA Cup final.
“This is a huge moment in the history of our women’s team, indeed for our club overall.
“We want as many of you there as possible.
“Your support has helped drive both the women’s and the men’s team all season and your support on the day is very much needed.
“Wembley is a special place and it’s a chance for you to be part of something unforgettable.
“Bring your family and friends, show your pride in the club and the city.
“Moments like this do not come around often.
“Come and be there with us to create a moment of history for the club and the city.”
Tickets for the Albion section are on general sale via the club website, priced £20-£30 for adults with concessions available.
Safe standing is available.