Alice's views on relationships were shaped by what happened with her parents.
To have little time to date someone was just the excuse, in fact her real reason to be so hesitant is how inadequate she feels to experience love.
She is a mafia boss, a criminal, responsible for terrible things and with no intention to change that anytime soon, a fearsome fighter and cold blooded killer.
Her father was the same and he had to keep this hidden from her mother, when the secret was revealed the mother couldn't take it, the person her father is, the same she became, was "not made to be loved" or at least this is how she sees the situation.
So she was terrified of opening her heart to someone if it meant to be abandoned when eventually the person couldn't accept who Alice is, this is what made her fall for Mc, he is at the same time someone who can live in the dangerous world she was part of and accept what kind of person she is, and more important, continue at her side despite that.