Hi dragonfly
I'm pretty sure you have nothing to worry about with regards the ivy. The tendrils which hold the plant to a surface are not true roots, they don't absorb water or nutrients, they just support the plant. Ivy roots are unlikely to be a threat to your liner unless you have a miniscule leak you're unaware of. Roots will follow a trace of water to it's source, but cannot "sense" water through butyl. If there's no leak, there's no water, and no problem.
By bulrush I presume you mean Greater Reedmace (the one with the cigar-like seedheads)? I'm aware that this can damage liners but I don't know how or why, or whether other plants can do so as well. The difference, maybe, is that where the ivy is outside the pond trying to get in (or not), the bulrush is inside the pond trying to get out

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As replacements for the irises, consider Purple Loosestrife and/or Meadowsweet. They go well together.
HTH
T2