Congratulations on successfuly litter traiining!!
I think that what happened with your dog and bunny has made your bunny extra cautious. I mean if you went outside, and a lion came near you and acted like he wanted to get at you, you might be a bit freaked out for a while. It’s survival instincts that keep us alive and are hard to shake if rattled. I have no doubt that the last time your bunny went out he was more on alert, and any little noise (even if you couldn’t hear it) made him run for cover.
So you could try a couple of more times to see if he’ll start to feel safe again, but if does not and it just ends up stressing him out, then give it a break for awhile.
An important note about bringing your bunny outside: Even with the xpen, be sure to cover it with a sheet or something for several reasons: This may make him feel a bit safer, protects him from birds of prey like hawks, and keeps him out of direct sunlight.
Also, be sure to check your bunny for fleas and mites on a regular bases, especially during the summer months, as they are more susceptible to these when they are outside and sometimes by the time you notice the fleas and mites on your own without checking, they have caused great discomfort and even infections. So just check weekly for fleas and mites. Sometimes you can’t see them, but you can see the debris they leave behind.
Also, always be sure to let all of your family members know you are out there with your bunny and to keep the dog away until your bunny is safely inside. Put a note on the doors, whatever it would take to prevent your bunny from ever being in danger by someone who may forget. Xpens can easily be pushed down by dogs, and not only that, your bunny can actually be scared to death without ever being in direct contact.