Having purchased the iPad with your account does not in any way link or associate the iPad it to your account.
When setting it up she would have had to log in with her account. Did she not do this? Did she log in with yours? Did you set it up for her with your account? Did she restore a backup from another device? Was that device ever logged in with your account? Seems like a bit of context is missing here, between purchase and now.
If however you ever used your Apple account to download apps onto another device she used for any reason and she used a backup form that device to set up this iPad, those Apps would remain tied to your account and require your account and password to download onto the new iPad and update later (the list of installed apps is stored in the backup, and will be used to download the apps onto the new device). The only way to resolve this, is to delete said apps from the iPad once they have been downloaded.
Also, make sure your email account is not set up on her iPad for any reason. If at any point you added your email account to the Mail App settings again to another service and she used a backup from that device to set up the new iPad it will restore email accounts onto the new device and request the password for them to access.
She can go to Settings ➜ Apps ➜ Mail ➜ Accounts. And see if your account is there and remove it.