It amazes me how people on these forums can be so judgemental. Yeah, I'm a student, but I'm also a grownup. You're not talking to some egotistical 20 year old that can't see past the end of his nose. I never said that I didn't have the money, see my OP. Just so you know, it wouldn't be 4K. OK. It's not like I want to hoard a bunch of basses. The Warwick would be sold and the money would put toward the Roscoe. Go flame somewhere else.
Who's flaming? If any of the comments here for restraint count as flaming, you should check out what goes on elsewhere on the internet. I think most of our comments suggesting that maybe you should practice self-denial vis-a-vis this bass began by saying, "If you have the money, why should she object?"
Since you're asking for ways to "sell" your wife on this, I would assume that, even with selling the Warwick, it's going to be a bite on your budget. If, after selling the Warwick, you can buy it, and it won't mean not being able to pay other bills, or not being able to spend money on other things you guys really need to be spending money on (new tires for the car or whatever), then I'd say all you need to do is tell her that. If she's a rational woman, you're all set. If she's not... well, you have other issues than how to buy a bass.
I feel that the money in a marriage belongs to the marriage. Each partner can, of course, buy themselves things that they want or need, within reason, but at the end of the day you need to ask if you're spending money in a way that's good for the marriage. Are there other things you should be spending money on (or saving money for) that would be a better use of the funds right now? College fund for kids? Paying down debts? Do the two of you really need a vacation? If so, I'd say you should attend to those first and the roscoe can wait until you've saved some more. On the other hand, if all those other kinds of things are in good shape and you can get the Roscoe without throwing other things off, then bless you and go for it.
I am apparently living closer to the edge than you financially -- a bass of that caliber is just out of the question for me. When I started off, I put about $150 into a used Ibanez Gio and a practice amp with the handle broken. I got my main bass as a Christmas present, and sold the first bass and amp to combine the money with some additional Christmas money to buy my amp. When I started thinking I would need a backup bass, I got a used MIM Fender P for $200. The Mrs saw it and said it was too much. I didn't want to let it go but she was absolutely right. I put new strings on it and fixed it up a bit (it was pretty beat up when I got it) and was able to resell it at a profit of $50, then bought a used SX with practice amp for $100, and then sold the amp off for $20. The outcome of all this is that I now have a perfectly decent backup bass which cost me a net of $30 (well, $55 if you count the cost of the new strings). I can justify blowing that on myself without feeling that I'm straining the budget.
The point is that this is the world I live in - so maybe you can see why I react as I do when asked how to justify buying a Roscoe...for $4000, or $3000, or $2000, or whatever you would wind up spending, I don't know. Watching the budget with my family means scratching for the $50 backup.