Fah Down Go Boom!

So my daughter got me a new bike for my B'day. okeedokee.
Of course I have some minor (sometimes) balance issues (thanks Mr. Asperger) which rarely if ever become a problem. But the other day, in the evening, coming home from work, I hit a sandy patch and had to turn somewhat sharply. And I was told that the tires weren't great.
BOOM.
On my side in the traffic. Ouch. Scramble. Ouch. Stand up.
Nothing broken or bent, either on me or on the bike. Good. But sore for quite a few hours. So I biked the rest of the way home. Opened the side door.
And then taking the bike down the stairs to the basement.
BOOM.
Geez. This is getting to be a habit. And very hard on the decorum/composure coefficient.
But nothing damaging really done, and one advantage is that after checking the bike the next day, I discovered how the brake-springs work to regulate the release. A positive, after all.
So my question of the day is:
Are balance issues common in Asperger's, and what coping strategies do you use?
Personally, I have discovered that I rely heavily on visual orientation for balance.
Sigh. That just means when I buy my next motorcycle, it better havce a sidecar!