is letting myibay access my ebay account safe? how do i know something won't happen, such as stealing my money?

As the developer I can say it's safe.
Myibay uses secure protocols for all sensitive transactions.

You provide access to your eBay account, not to your bank account or PayPal account so there is no way to steal your money.

If you still don't trust it, you can always register a new eBay account just for bidding and use it with myibay.