This is a difficult question to answer with the information you've supplied so far.

Assuming that you have a rear wheel/freehub/cassette combination that you'll be running, you'll have to measure the chainline to the center-most cog when installed. For an 8-speed, this will be in the gap between the 4th and 5th position. For a 7-speed, this will be the 4th cog.

Measure from the inner distance between the two rear dropouts, both ways. Do the math do determine the millimeters from the center of the dropout spacing (likely 63mm from the non-drive side dropout inner face) to the cog in question. This is your nominal chainline. So, for your double, you'll want to straddle this chainline for the front crankset chainrings. If you have ~4.5mm to 5mm separation between your chainrings, then, factor that into your determination of the correct chainline. Align the center of the separation with the chainline measurement from the rear.

Now to the empirical part. Let's say, for discussion, that your desired chainline for the front is 48mm. That's the goal.

Install your existing spindle (the one you've just removed) with its bearings and the cups/retainers tightened properly. No need to worry about lubrication. Install the right crankarm with chainrings and measure the chainline. From the drive side outside of the seat tube to the center separation between the chainrings, in millimeters. Add to that measurement half the diameter of the seat tube. That's the current chainline. How much is it off from your desired goal? Write it down, in mm.

Remove the drive side crank and bb spindle. measure the spindle length, taking into consideration any asymmetries (you said it was from a triple). Add (subtract) the difference between what you have and what you desire, and that's your answer, the correct spindle length for your double.

Order a cartridge of that size that fits the threading and width of your bottom bracket shell.

Does this help?
PG