In theory, with 48 people, you only need 3 byes if you slightly change the order past the semi-final round.
Winner's Bracket:
Round 1
48 teams (24 winners, 24 to Round 1 Losers)
Round 2
24 teams (12 winners, 12 to Round 2 Losers)
Round 3
12 teams (6 winners, 6 to Round 3 Losers)
Round 4
6 teams (3 winners, 3 losers to Round 4 Losers)
Round 5
3 teams (1 bye to the team with the best overall Win / Loss, 1 winner, 1 Loser to Round 6 Losers)
Round 6:
1 + 1 = 2 teams (1 winner, 1 loser to Round 8 Losers)
Loser's Bracket:
Round 1
24 teams (12 winners, 12 eliminated)
Round 2
12 + 12 = 24 teams (12 winners, 12 eliminated)
Round 3
12 + 6 = 18 teams (9 winners, 9 eliminated)
Round 4
9 + 3 = 12 teams (6 winners, 6 eliminated)
Round 5
6 teams (3 winners, 3 eliminated)
Round 6
3 + 1 teams (2 winners, 2 eliminated)
Round 7
2 teams (1 winner, 1 eliminated)
Round 8
1 + 1 teams (1 winner, 1 eliminated)
Championship:
Best of 5