Don't be embarrassed, just watch the elements around you: water, earth, air as you move or meditate. You may well inspire somebody passing by, but most importantly, you could inspire yourself :-)
For outdoor yoga you will need:
- base mat for the grass/mud/sand, a cane beach mat is cheap & easy to find, then when you finish your practice don't roll it up, fold it into to itself so it doesn't get you and your other things muddy
- your usual yoga mat goes on top of the cane mat
- jumper/something you can wrap around your waist or shoulders as you practise then put back on for your meditation or final relaxation
- as little else as possible... shoes and door key if you're going far, otherwise just barefeet to step out to your garden... start carrying a bag, a book, sunglasses and it's a faff you don't need, keep it simple :-)