Now you're really into gremlin chasing, and why I'm not a fan of trying to GFCI everything. A few options
- Disconnect the conductors from the dryer receptacle and see if the breaker still instantly trips. If it stops, it could have been a wiring issue in the box or at the receptacle.
- Megger the cable to the dryer outlet to make sure it doesn't have a staple though it someplace.
- Shut off the other breakers in what looks like your service panel and leave on only the dryer breaker. See if it still instantly trips.
The GFCI breaker connects to the neutral bus because it watches the current going out on the hot(s) and coming back on the neutral. What goes out should come back. If it does not, there is potentially a ground fault someplace and it trips as a precaution. The challenge is that your service panel should have the neutral to ground bond which occurs in service equipment. I can't help but wonder if you are getting a small amount of objectionable current via that bond. It's kinda like wiping a booger on the wall. One ain't a big deal, but 100 is gross.
How far is it from your service panel to the dryer? There's also a phenomenon called preloading. On a long enough circuit, you can get little amounts of leakage current or capacitive coupling which are mostly harmless, but add up (much like wall boogers). It makes your GFCI start out much closer to nuisance tripping.