Curious figure of speech...

Hi!
I hope I've come to the right place for help.
I'm not a native English speaker but I do try and read a lot of English. I'm reading this book and came across a figure of speech I'd never come across before and is baffling me (quoting the whole line it's part of for reference):

And, if like me, he travelled on the number 38 bus as well as the 19 (you get my drift) then a comely little piece like Aggie was surely more in the grizzled old fellow's line.

From the context I *think* the implication has to do with bisexuality. It's said by a male, bisexual character (the 'me') about another male character (the 'he') whom he thinks is coming on to him as well as to a female character (Aggie).
I've tried googling the phrase, but only came up with London bus time tables. In case it makes a difference, the character is British and the setting is 1940s.
Can anyone shed light?