When I eneter a shop and bribe with any it shows a random number of gold to the right of the NPC's name. Does anyone know why it shows that?

Do you mean at the bottom of the dialogue box that appears when buying or selling? This is the maximum gold the merchant will trade for in one transcation. Meaning that if, say you wanted to sell a Mundane Ring to an innkeeper with only 50 gold, the maximum you would get for it is only 50 gold, which is a terrible idea considering it has a base price of about 12000. This feature means that most high-end items you will never sell for a good price, as the maximum barter gold is 2000, with a plug-in merchant (from Battlehorn Castle, Wizards Tower etc.) with Expert and Master Mercantile perks. For any other questions, go with UESP.

That is the max amount of gold that the merchant has available to her/him. That is, per transaction.
So while in the buy/sell window, you could sell one glass long sword for 800, regardless of its true value, and sell another glass sword for another 800, one after the other.
There are other merchants who have a higher starting amount of gold. Look around. I usually used to use Agnete the Pickled in Skingrad, whose base gold was 1,200. When you get to level 75 in Mercantile, you can increase the amount of money that each merchant has, by investing 500 gold per shop. Which gives Agnete 1,700. Supposedly if you get Mercantile up to 100, you get another 500 on top of that, but I've never been there. Closest I've been is about 85 ish.