I've got two telescopic webtex bivi poles. Now, I haven't used them yet so my advice is probably a bit useless, but what I really wanted to say, from the bottom of my heart, with all honesty
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is that even one of those webtex poles would be a bit cumbersome to carry on the bike. They're longer than you expect, even when fully folded, they're heavier than you might expect and they're slippery, so wouldn't be the easiest thing to tie up on the rear of a saddle bag.
( I assume one of the nice things about tarp camping is that you can camp ultralight, so wouldn't think you'd have a full set of pannier bags? )