Budgies need both seeds, pellets, and additional vegetables each day to be healthy.
About 1-2 teaspoons of seed per day and unlimited pellets is the end goal, however, it takes time for budgies to be weaned onto pellets. Check out the budgie diet stickies for more information.
Since her cage is covered at night, it should be just fine for her.
As for baths, budgies should never be forced to bathe nor do they need to. Budgies (and all parrots) are very clean and they keep themselves in good shape by preening with their beaks. Some budgies do enjoy bathing, however, so you can offer a shallow dish of water of about room temperature (during hot days it can be a little cooler but not cold) sometimes and see if she'd like to bathe. If not, that's fine.
Budgies need about eight hours of sleep a night, which it sounds like she's getting most of the time, but they like to make up the extra bit as naps during the day. So she's totally fine
You can also find a lot of other great budgie information in the Stickies and Articles around the forums! Feel free to post any other questions you have in this thread.