PearlJamNoCode said:
Star San is kind of expensive and I know its reusable.
These two statements are almost contradictory. A small bottle of Star San is the same price as a small bottle of One Step (for example) and lasts MUCH longer, especially if you save it.
PearlJamNoCode said:
I'm thinking that using the same 5 gal batch of it on brew day and then bottling 3 or 4 weeks later.
Let's assume for a moment the bottles are already extremely clean and that you've got some kind of bucket with a lid (bottling works!)... I see no reason you couldn't sanitize your bottles, your carboys, your spoons, hydrometer for a few batches.
I keep a 5 gallon bucket of Star-San solution (1 ounce to 5 gallons, 36 ounces to a $20 bottle...) ready at any given time with my funnel and carboy caps and airlocks floating around. I dump it after three batches (full process) simply for peace of mind.
PearlJamNoCode said:
During the interim would it be safe to store in a spare bottling bucket?
Assuming it's clean, yep!
PearlJamNoCode said:
Would that damage the plastic or effect its sanitizing effectiveness?
Star San is pretty safe for use on just about anything in a "normal" brewery. It won't damage plastics. On the flipside, any plastic that can harm Star San (dirty, has holes, scratches, is on fire) is probably not something you'd want contacting beer anyway.

Star San can, over time, corrode metals when in prolonged contact.
Star San works because of it's acidity, as long as the pH stays below 3 it's effective.