You don't actually burst to avoid getting killed.
You DON'T burst to not take 150% damage and to have some barrier.
Bursting in BB is pretty much a shitty choice most of the time. Anyway, at the level you're playing at, bursts shouldn't get baited as much as you're saying.
I get what you're saying, but you need some proactive choices, not just stand back and be afraid of closing in. The moment he gets his sparkball, the matchups is going to look a lot more shitty, so you're better off getting as much ground as you can before that.
I don't know the startup of Tager's backdash, but if he manages to backdash>grab you in the middle of your strings, you should probably try new, safer strings. As a general rule, never do a 5C in a string if you're not sure the distance is good enough to avoid being grabbed. 5A, 2A, 5B and 2B should be your main tools as long as you haven't pushed Tager back a good deal. Dash in J.C (like you did at 0:19, 0:25, 1:18 and 1:29) is an exceptionally shitty idea against Tager, for example. A normal jump would accomplish the same thing and leave you way less open. If you really must, add a falling j.D, which should, accounting for the landing, leave you in a position of slightly unfavorable reset (better than the position horizontal j.C alone will leave you in, at least). Remember that when you IAD in the face of the opponent, you're giving up your second jump, which is in many cases a vital defensive or offensive option. You're basically saying "fuck mindgames, I'm in your face". This is also the case for Hell's Fang, which CAN be backdash-punished by Tager. Competent tagers will make you pay for this sort of things dearly.