It doesn't include hotel pick up or drop off, you can easily take a taxi, but you can book tours through the official website.
Hey, good to know about your trip. There are a lot of tours available as per your requirements. Unfortunately I don’t have any experience with guided tour with hotel pick up and drop so I would suggest you to just take a look at Google search. I also found some results which look quite helpful to me. Take a look here https:/… tripindicator.com/tours/rome/best-colosseum-… or may be this https://www.museumsrome.com/en/guided-tours-… Hoping that you’ll find what you are looking. And yeah, please share your experience here so others can also get some help.
I agree with Donna, take a taxi to the Colosseum. It's 5 Euro p/p for a tour (plus admission).
From the official website - https:/…colosseo-e-shop.cfm :
Individual tickets with scheduled entrance time and guided tour
Explore with our archeologists the history and the characters that used to enliven the arena of the best-known amphitheater of the world and the heroic deeds of the gladiators during the years of the Roman Empire.
Participation fee: € 5,00 + admission ticket to the site
Duration: about 45 minutes
Participants: up to 40
Language: Italian, English, Spanish, French