There are a few things you can do and not be punished for it as long as you’re not abusing them. For example after a light or two, go for an ambiguous cross-up, it’s hard to AA, like some Blanka/Adon players like to do, jumping around you until you make them pay for it.
Try dashing forward behind a fuhajin on guard or doing instant divekicks to go back in, but it’s the same, you’ll get punished if you abuse them.
With 2bars, you can FADC Senpushas to keep applying pressure, something like cl.HP xx light Senpusha > FADC if HP blocked. If HP landed, you’re in an ambiguous cross-up position which allows you to keep pressure going. Or simply 2MK xx HK Senpusha xx FADC > throwbait if blocked.
If you land a hk Senpusha, you can try to do the max range “safejump”, then a Sekku, and then a 2MK/HK or and instant divekick for example, it’s a range not too close that I find to be at Juri’s advantage.
After a backthrow, take around 2 steps forward then jump for and ambiguous cross-up, most shoryukens will whiff.
After a MP xx Store > EX Senpusha, you can do dash > release > dash > light Senpusha, it’s not always safe, but it’s a good trap, catches people trying to jump, frame traps, and it’s hard to punish the max range Senpusha.
Save MK Senpusha confirms for when you want to go back to zoning, if you want to keep pressuring, use light Senpusha, and try a frame-trap, dive or a karathrow behind it. You can reset a highly damage reduced combo with Senpusha xx FADC xx cl.MP xx light Senpusha > Kara-Throw.
After cl.MP xx Store, you can go for cr.MK xx Release, most match-ups can’t reach you at that range within 7f, and the 2MK recovers fast enough to deal with a jump-in with a dash under or kasatushi.
You can use moves that leave you out of poke range and dash forward after them, like after a far.MK or a far.HK. You can cr.HP if you see a neutral jump.
Finding “strings” that catch/reset jumps is also quite useful in keeping pressure going. At -1 you can use far.LK or far.MK and reset a jump start-up, for example after Store/MP/2MP, and react with a dash to get back in. Light Senpusha works too I guess, as long as you use it from max range and not from a cancel it is hard to punish it.
MK xx Store(mid) > lk Senpusha > pause > release for a meaty mid Fuhajin > dash is a less damaging knockdown but allows to keep pressure going compared to the EX Senpusha juggle.
Random FA can help you keep the pressure going too.
That’s just a few ideas I could think of, but yeah, Juri is not suited to rushdown, most of her BNB knockdowns don’t place her in a decent situation to keep applying a decent wake-up game unfortunately unless you nerf your damage badly to be able to do it. And a decent player won’t fall for her tricks and punish you hard.
I’d say save the rushdown for the corner, she becomes much better there (decent mix-ups after Senpusha knockdowns, unblockables after throw, able to stay in longer…), or after activating FSE of course.