you do realize that there's a 99.9% chance danny had bob baby singing into one of his beloved u47's > neve,right? that in itself plays into the huge round mid presence. but yes ditch the delay and create an aux with a large verb with a longish pre-delay and have her on the mic to where it's displaying some proximity effect. from there create some automation on your verb send or returns and help breath some life into by increasing and decreasing the amount of effect present on the vox.
There's also the fact that she is a female vocalist, with a quite piercing voice. Whereas Bob Dylan is a male vocalist with an old man's low deep growly baritone.
Even more so - and this is the most important thing - Bob isn't really singing on that track, so much as whispering into the mic. Whereas your singer is really singing and emoting.
They're polar opposites.
I would put a high shelf on your singer's voice, draw a small EQ bump and try to find a low-mid (or possibly even a high-mid) sweet spot that gives her voice a bit more warmth and body.
If you can't find it then I would re-track, and get her to sing a lot more quietly, which in itself will add a fair bit of bass. And concentrate on singing from her chest: take big deep breaths in between lines.
If the instrumentation isn't already panned hard left and right, then try it, and make sure her vocal is absolutely dead-centre. You could increase the delay between the left and right guitar, which sometimes creates the illusion of an even wider space. And turn the instrumentation down a touch.
i'm not a pro or anything, but i think that your track is present enough. maybe too present. Also, i think that the Dylan snippet is darker than yours. I believe that if you were to fill out the low and low-mid frequencies your mix would sound much better in the top end. I think it's all about balance...you know, frequency-wise. also, i would lowpass or shelf the highend of the delay. or... you could probably pull it back a tad in level.
BTW, I would use the joan osborne version of this for a reference. It sounds very very good. listen to what they did there.