As John was studying a bus timetable

[Bassim]

I am wondering if my sentences are grammatically correct.

As John was studying a bus timetable, an old woman came up and started pestering him about bus lines. John thought she was really not interested in bus traffic but was lonely and searched for company.

 

[Charlie Bernstein]

I am wondering if my sentences are grammatically correct.

As John was studying a bus timetable, an old woman came up and started pestering him about bus lines. John thought she was really not interested in bus traffic but was lonely and in search of company.

That's the most common idiom. You could also say "searching for." That would be natural, too.

 

[GoesStation]

Looking for company would be more natural than searching for company.

 

[emsr2d2]

Or "... and [just/only/simply] wanted [some] company".

 

[Rover_KE]

There are a lot of buses in two sentences. You could lose one of them by saying '...not really interested in what he was looking at'.

I'd say bus routes rather than ​bus lines.