I never thought about it before, but I think you are correct.
I didn't see anything wrong with "by a" at first, but in fact have never heard it before, when I stop and think about it.
I do wonder if there is some obscure "rule" on the subject? (I checked the definition of "by" in this usage, and it is "on" - and not "on a" - you can say, he came on a camel, but not he came on camel. So why isn't the "a" used? Curious language we have, eh?)
She comes by a local van but goes back by a private taxi.
Shouldn't it be 'in' in both cases since the article 'a' is used?
Thanks in advance.
Yes, you are completely right. Here the use of the article 'a' rules out the preposition 'by'. You could say naturaly 'She comes by van but goes by taxi."
I guess here the preposition 'by' only gives you the transportation means, in general terms, but does not specify exactly which unit. So you say:
"He goes to work by car every day. Today he will go in his friend's car."
"She usually goes by bicycle, but today she is going by car."
"But, how will I find her, there will be hundreds of cars arriving this time."
"I guess she is going in a red car."