No need to guess, it’s all outlined in the bill:

1. ByteDance has 270 days (+90 days at president discretion) to divest of TikTok and sell to an entity not affiliated with an “adversary country” (China, Iran, Russia, N. Korea).
2. If they don’t sell, hosting providers of TikTok application (servers, storage, app store, etc) will be fined up to $500 times the number of users in the US if they continue to host the application

So basically, the law will impose a fine of US hosting providers of the app. If the app moves all services overseas to foreign entities, then the app presumably will continue to work even if banned if already installed (plus the website if hosted overseas).

ISPs and search engines are explicitly exempt from the bill so there is no mechanism to ban connections to TilTok servers or links to TikTok.