Ah, that's very likely a tinted toner, rather than a stain or dye.
I should think it will be easier to get that kind of effect with basswood than with poplar, given poplar's tendency to have a lot of green streaks. Usually you see basswood and poplar with solid colors because they are so visually uninteresting compared to other species. [/size]Obviously you'll want to pick up some lumber to experiment on. Poplar and basswood are both pretty cheap, and available at your local big box home improvement store in small project precut sizes.
But I got that kind of result on my green tele (after a great deal of experimentation) by making a stain out of Mixol universal pigment in a vehicle of 2:1 lacquer thinner and lacquer retarder. That was on mahogany, though, and I'm not sure how well basswood or poplar will take a stain. This example was done using Mixol No. 13 Grass Green.
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Another approach you could try might be to seal with an initial coat of tru-oil, to avoid uneven uptake of the color, and then apply a number of tinted coats of Tru-oil to build up to the color strength you want. Then topcoat with more Tru-oil once you get the color where you want it. Again, experiment on scrap. It's a lot easier on the ol' ticker when you screw up.
Given Tru-oil is a polymerized oil, you might even be able to use artists' oil colors as your pigment if there's a particular shade you like. That might save you the headache of trying to get to the desired shade of blue. Just thinkin' outside the box here, having failed to achieve desired colors with pigments myself. Blending is hard, and requires actual recipes or life experience to get it right. I know from experience the Mixol No. 9 Blue is not as rich as the blue in your example. You'd need to combine with some purple and black to get it where you want it.
