I would suggest that you should have a BR of at least 20 buyins for smaller tournaments of fewer than 300 players, and 50 buyins for larger games (because a larger player pool increases variance).
If this is too limiting, because you don`t have that amount of cash available, try playing in a small-stakes ring game until you win the buyin for your tournament.
If you are a winning MTT player, a full-ring game of 25NL or 50NL should be easily beatable for $10 or so with a little patience even though cash games are not your first love. You then, in effect, have a free buyin for a $10 MTT. Repeat this process until you reach a final table in your MTT. That will then boost your bankroll enough that you can drop the cash games and focus on tournies exclusively.