You don't necessarily have to escape in order to not die from Rupture, you should generally be altering your whole play strategy when there is a BS on the enemy team, just like if there were a Riki or a Techies - you simply can't play the game "as normal" and expect to get away with it.
The first thing is to carry a TP scroll. If you do get caught, especially early game, you can often just TP away before he has time to kill you.
Next, you should be on the look out and be aware to when you're vulnerable to a rupture and when you're likely to have one cast on you. Don't wander around with low health, along in the jungle as this will make you an easy target. Try to keep some health and try to stay with your team to avoid getting caught alone. If you can't see BS on the map then assume he's nearby.
If it makes sense on your current hero, buy a Eul's Scepter. It can buy you time either to use it on yourself and make yourself temporarily untargetable, or use on BS and give yourself time to TP away or get your team to come and help you.
Again if it makes sense, build a Pipe of Insight to mitigate some of the damage.