Is Bitvice able to access my Bitcoin in my wallet?

No.

The only details that you submit to Bitvice concerning your personal Bitcoin wallet (to which your purchased Bitcoin is sent) are your wallet public keys. With this information Bitvice can only send Bitcoin, but cannot access or control your wallet by any means. As long as you keep your private keys (12 or 24 words) private from anyone else, you and you alone will have full control over your Bitcoin.