I too have re-built a few bamboo rods. I have found that manually stripping the finish is better then using chemical agents on older bamboo because there is less chance of de-lamination.
The easiest way that I've found to strip the finish off these old rods is to use a utility razorblade. Place the blade perpendicular to the shaft on the flat of the rod and pull towards use. This action scrapes the varnish off without effecting the glue. Do take care not to nick the bamboo or scrape across the edges, thus rounding out the shaft.

I've restored a few bamboo rods and have acquired some info from some professionals. You're safe using a chemical stripper, you just want to avoid acidic types like aircraft paint stripper. I use CitrusStrip from Menards. Brush it on, leave it on for 2-3 minutes, then wipe off. Reapply over tough spots. You can use 0000grade steel wool to smooth down rough spots, just be careful not to round off the corners of the cane. CitrusStrip also has a clear "rinse" solution you should use to wipe down the rod after stripping. This neutralizes the stripper. When done, let the rod dry for a couple days before rewrapping & varnishing.