You don’t need to install Linux or anything like that. API requests are just HTTP requests, they can be done from pretty much anything with an internet connection, or any operating system, in almost any programming language.
The Getting Started guide to the API explains how to send your client id as a header when making requests: https://dev.twitch.tv/docs/api
And if you make a request to the Get Users endpoint https://dev.twitch.tv/docs/api/reference#get-users using your bots name as the login param you will get a result back containing your bots user ID.
That being said though, why do you even need to be verified? Bot verification is only for accounts that have a specific need to have increased rate limits, personal bots are unlikely to be given verified/known bot status as the default limits are perfectly reasonable for bots on a small number of channels. If by Verified you mean so you can get the verified check mark next to the bots name, you wont be given that.