The bill applies to only to financial transactions ("covered transactions" in the bill) and holdings ("covered holdings"), there's nothing in it at all directly regulating access to data or websites by individuals.
Here is the definition that the bill uses for "transaction":
> (17) TRANSACTION.—The term “transaction” means any acquisition, importation, transfer, installation, dealing in, or use of any information and communications technology product or service, including ongoing activities such as managed services, >>>data transmission<<<, software updates, repairs, or the provision of data hosting services, or a class of such transactions.
As you can see here, mere data transmission is considered to be a transaction. I strongly suggest that you read the bill, in its entirety.
If you're not going to be banning internet services, how can you possibly ban TikTok? It has a website, you know.