Bursting is very hard to do well with stain. It's very hard to blend two colours, so practice on scrap wood first. You really need to get the lighter and the darker colours on wet at the same time so they can blend in the middle where they meet. Otherwise you can try airbrushing the darker stain on.

Tru-Oil will certainly re-absorb some stain, so if you use that on a stained burst, I'd suggest using a brush for the first few coats, brush from the centre to the outside of the guitar so you don't bring dark tinted TO into the middle. I'd even leave gaps between TO brush stroked for the first couple of coats and fill them in with the second coat, again using a brush. Brush once each time, don't go back and forth which will muddy the finish. Once you get a few TO coats on, you can stop worrying about the stain bleeding.

You can of course, spray paint over a stained base, then use Tru-Oil on top. Easier to get a good burst that way.

This is the sort of tape to use for the binding, 3M 471 tape. https://www.amazon.co.uk/Fine-Vinyl-.../dp/B00CUPL8BI
It comes in 3mm and 6mm widths. Other makes are available.