Hi and welcome, pippin pony!!
Anything you do with your horse will build your relationship, as long as you present yourself to her as a consistent, confident leader. As far as specific activities and exercises, all things in moderation, and with appropriate execution and safety/equipment considerations. If your pony is relatively young, be sure not to stress her joints with too much circling/jumping too soon. Protective boots are worthwhile as well, if she isn't already outfitted with them.
In terms of tackling new or troublesome environments, like riding on roads, the confidence of the rider can make or break the experience for the horse. A confident rider in the saddle can make all the emotional difference in the world for an unconfident horse in a potentially scary situation. Even if you're feeling unconfident, do your best to not let your mare know it!
Keep smiling, breathe deeply, and ride
. If your mare sees you as a leader, she will accept your confidence as assurance that there are not pony-eating-monsters out to get her, just as she accepts the authority and protection of a dominant horse in a herd situation.
If confidence on roads is something that you and your mare really struggle with, I recommend finding a confident horsey friend on a seasoned, bombproof horse to go out with you. Sometimes seeing another horse do it first and come out alive and unflapped does wonders for nervous nellies.