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So this is the progress of my Bush Champion cucumber plant. Talk about a growth spurt !!
Can anyone tell me though, what is the stringy looking thing that has been only there for two days !!
Yep, you read that right, it took two days to flourish.
Thanks.

I can't see your picture, but I think the stringy thing you're talking about is called a tendril. The plant uses them as a climbing and holding "anchor". Most cucurbits produce them. Even bush varieties. Bush varieties will still climb some, but trellising isn't necessary.

AH! I see it now!
Yeah, that's a tendril!

Is it okay to keep it like it is, as I am growing the plant in a container, or do I have to trim it/cut it?
As far as I understand, this type of plant does not need support, so would it be better to put the container right up to my balcony fence and encourage the tendril to grow there?

I wouldn't cut it.

You can trellis it if it suits you, but it's not required. The more upright you keep it, the straighter your fruits will be. It'll try to climb, but it won't go more than a couple feet.

Thank you Lindsay for all your help.

Welcome!