How to break loop inside a promise?

Assuming you want to call the compares sequentially, this will do it:

.then(function(answers) {
    var compare = Promise.promisify(bcrypt.compare),
        i = 0;
    return Q(false).then(function checkNext(res) {
        return res ||
               i<answers.length && compare(answers[i++].password, user.password)
                                     .then(checkNext);
    });
})

It will "recursively" step trough the answers array, stopping on the first true result. To return the correct answer (instead of just true for "found") or null (if not found) like @Noseratio's code, you could use

    var i = 0, answer;
    return Q(false).then(function checkNext(res) {
        return res ? answer : (i<answers.length || null) && compare((answer = answers[i++]).password, user.password).then(checkNext);
    });

or better the more verbose

function next(i) {
    if (i < answers.length)
        return compare(answers[i].password, user.password).then(function(res) {
             return res ? answers[i] : next(i+1);
        });
    else
        return null;
}
return next(0);