and showing the reader what an ignorant and stupid fool he is.

He probably thought it was 'cool' to mention Bedford. Perhaps it was a place haunted by the students at Oxford?

We have to remember he is a college student at Oxford, and the likes of JT have to find their place among people like Darcy, Bingley, Tilney etc. people with money there.

JT talks for effect. Mentioning names of people and places to impress.

JT is not well informed - he gets swindled when buying a second hand carriage - he obviously knows nothing about such things, so I doubt he buys and sells things to advantage, which reduces what I thought would be additional income for him.
Can he afford going to Bedford?

Another interpretation is that, when Catherine asks him how he knew him;
“Know him! There are few people much about town that I do not know. I have met him forever at the Bedford; and I knew his face again today the moment he came into the billiard–room. One of the best players we have, by the by;

Here Thorpe wants her to think he moves in high circles and has known the General forever, while perhaps they met in the billiard room at Bath.
I wish we knew who the gentlemen were of whom he talks about earlier - Freeman, Jackson of Oriel - men who wanted to buy his gig. I am sure they were some rich important men at Oxford.

As Carolyn as mentioned in her post;
[John is a master hyperbolic utterances,

We can't believe what he says.