Here's info on the subject of eggs:
http://www.redearslider.com/reproduction.html
And yes, females lay eggs whether there's a male present or not. The difference is, if there's no male they won't be fertile - they will never hatch.
If she's wandering around in a garden every day, she should have plenty of opportunities to lay eggs if she needs to. I'm assuming there's plenty of dirt, some of the dirt is soft, and there are sheltered places like underneath bushes. Is this right? Have you noticed her trying to dig a hole with her back feet?
When she wanders in the garden, is there any chance at all that she could get into chemicals - fertilizer, pesticide, herbicide for instance? Are there any ants or bees in the garden that could hurt her?
And....excuse my ignorance, but where is BKK again?