cab from Heathrow to the Bloomsbury area of London

Well, it's not to take a cab, that's for sure.

Get on the Underground (Piccadilly line) at the airport, and ride it to either Holborn or Russell Square. You don't even have to change trains. The hotel is a short walk from either station.

From Heathrow airport to Mercure London Hotel Bloomsbury it takes Approx.59 mins by bus to reach and it is quickest way to reach from Heathrow airport as the bus facility is available for every few mins from Heathrow airport. But be aware of changes in Transportation facilities at Heathrow terminals.
From Heathrow airport to Mercure London Hotel Bloomsbury at WC1 it takes 1 hour to reach by car via M4 and hiring a car is easiest way to reach.

Maggia, that is contradictory....

You could send an e-mail to your hotel and ask if they would arrange a taxi for you. A lot of hotels have a preferred taxi service to use. You will be given a guaranteed price to/from your hotel. Then if you are caught in traffic, with the meter still running, you won't be shocked at your hotel destination. I also recommend Blacklane.com. You can go to their site, enter your information and get a fixed price also. You are under no obligation to inquire. You will have a private driver who will meet your where you pick up your luggage. It is an advantage to have a private driver, as you won't have to waste time dropping off/picking up other travelers.

She may just mean a private hire car, ie a minicab. Not self-drive.

We will never know - which advice met what was actually meant or which was used - as aj granito has never returned to either of his/her threads....