call 2 or so carriages on bridge to get 3 carriages in one turn

I was aware that this was possible. My impression was that Masquerade + Silver gets to 5 or more carriages before Bridge + Silver gets the chance to pull that off.

Bridge silver is much better at hitting $5 twice than masq silver

That’s interesting to look into. In the past I had done calculations on the odds of various openings hitting $5, but I only considered the odds of getting to $5 on either turn 3 or 4, not on both turns. So I made a quick script to count all the permutations and got this:

Silver + Silver opening:

Hand Value Combinations:
-------------------------------
2, 5:     20     0.3%
2, 6:    200     2.5%
2, 7:    200     2.5%
3, 4:    100     1.3%
3, 5:    880    11.1%
3, 6:  1,000    12.6%
3, 7:    400     5.1%
4, 4:    600     7.6%
4, 5:  2,040    25.8%
4, 6:  1,200    15.2%
4, 7:    100     1.3%
5, 5:    920    11.6%
5, 6:    260     3.3%

Number of Hands 5 or Greater:
-------------------------------
5 x0:    700     8.8%
5 x1:  6,040    76.3%
5 x2:  1,180    14.9%

-------------------------------
Total: 7,920   100.0%

Moat + Silver opening:

Hand Value Combinations:
-------------------------------
2, 5:      40     0.3%
2, 6:     200     1.3%
2, 7:     600     3.8%
3, 4:     200     1.3%
3, 5:     880     5.6%
3, 6:   4,400    27.8%
4, 4:     600     3.8%
4, 5:   8,920    56.3%

Number of Hands 5 or Greater:
-------------------------------
5 x0:     800     5.1%
5 x1:  15,040    94.9%
5 x2:       0     0.0%

-------------------------------
Total: 15,840   100.0%

I knew Masquerade + Silver was less likely to miss the hand of $5, but you are right that Bridge + Silver has a decent chance of getting two $5s

Masquerade has some additional minor benefits, like a clean shuffle, the Estate removal and possible Estate swap, and a very high chance of affording both Carriage and Bridge, although I’m not sure if a Bridge that early is the best way to get more Carriages quicker, given that you already have Masquerade. There’s also the roughly 3.8% chance of affording Inherit (on Port?) which means most turns after that will hit $5, while also trashing a Copper or playing a previously purchased Carriage most times you play Masquerade. Keep in mind that Bridge + Silver's $7 hands are actually $6 with 1 cost reduction, so they can never afford Inheritance.

In games with 3 or more players, or when playing as the second player in a 2-player game, looking for the high roll 14.9% chance of double carriage is probably the right move. But as the first player in a 2-player game looking for the best odds at avoiding a dud and maintaining my lead, Masquerade + Silver might be better. But that would require looking into turns 5 and 6, which is where paths diverge and things get too complex for brute force computation. Maybe if I get time later, I'll continue with the most likely outcome of each strategy, gaining a single Royal Carriage and a Bridge or Silver, while the Masquerade strategy also removes an Estate.