Mine is... wake up... doing my bits....
Leave.... walk 18 minutes over Tower Bridge (London) boom... at work in the city!

I do but my job is almost next to the train station.

I work from a home-office, so...

I have a short 5 minute commute, 7 if traffic is bad.

As for your situation, 10K a year is more than worth the 20 minute increase in an already long commute. However, if it were me going from 5 minutes to nearly a half hour commute I would not accept it unless there was a public transportation option that did not involve taking the bus.

Is the question in the title correct? 

45-60 minutes each way to and from work by bus.

Approximately a 50 minute drive, as it's about 50 miles.

10k bump in pay with employee car and gas card abilities? Those are all nice however don't look at your 10k bump in actual terms. You have to take into consideration the actual increase in your earnings and decide if that justifies the additional time. 

On face value I'd take it however it's not something that I would decide until I ran those numbers and understood the restrictions on the company car. 10k is 10k but a lot more goes into deciding to take new positions than dollar signs. 

40 minute train ride to school.

You better do it, that's a sweeet deal.