New Year Chaos (HackerRank problem) - find minimum swap count
Some minor stuff:
This if:
    if simulated[i] == q[i]:
        continue

is redundant and can be removed, due to the predicate on your while. The while would execute zero times and have the same effect as if you continued.
The while itself:
    while(simulated[i] != q[i]):

should drop the outer parens.
The range here:
for i in range(0, len(simulated)):

should drop the 0,  because that's the default.
Since you use both i and simulated[i], you should iterate using enumerate instead of range (though this won't be the case if you delete the if; continue). Getting a value from enumerate won't be helpful during the value swaps that you do later.
About the value swaps, this block:
        if i + 3 == q[i]:
            simulated[i + 2], simulated[i + 1] = simulated[i + 1], simulated[i + 2]
            simulated[i + 1], simulated[i] = simulated[i], simulated[i + 1]
            bribeCount += 2
        # do 1 bribe
        else:
            simulated[i + 1], simulated[i] = simulated[i], simulated[i + 1]
            bribeCount += 1

should collapse to
        if i + 3 == q[i]:
            simulated[i + 2], simulated[i + 1] = simulated[i + 1], simulated[i + 2]
            bribeCount += 1

        simulated[i + 1], simulated[i] = simulated[i], simulated[i + 1]
        bribeCount += 1