One type of wood bleach will definitely help get the paler parts to white or nearly so, but they may also have an effect on the darker streaks you want to retain. The green especially I'm sure will be affected as some people specifically bleach to remove the green from poplar, I suspect the purple will be lightened also (possibly to the point of disappearing entirely) but I'm not certain.
A previous Question has some related info: Chlorine bleach on poplar.
Also see the section titled Turn green to gold on Make Poplar Look Pretty on Popular Woodworking and Get the Color Out With Wood Bleach on Wood Magazine.
(Oh and finish it with a non-staining oil or whatever, maybe lightest shellac or danish oil?)
If you want to keep the colour as pale as possible none of the normal oil finishes would be the finish of choice, because they all impart a distinct amber/yellow colouring. Also note that over time this will always increase, never diminish*.
Of the things you mention super blond shellac would give you the best colour, although even this will tend to add a slight yellow or 'honey' tone.
Most waterbased finishes are "water-white" and will produce next to no colour change so are often chosen for very pale woods where lacquering is not an option.
*This is especially important to note for users of tung oil who may be using it specifically because it's lighter in colour than BLO tends to be.