When I click an item in the Shopping tab, I get a confirmation popup with the buyout price.

I'm unable to find a way to get the bid price into that popup, which means I have to switch to the Blizz Buy tab to actually post a bid. Example:

 
Most likely there must be a way to do this, and I'm just blind 🤔

In case I'm not blind, my suggestion would be something like this:

 
…or maybe just: clicking the buyout price (buyout column) selects the buyout price, and clicking the bid price (bid column) selects the bid price.

Edit: Added Right-clicking as alternative.

You can click on the item's name/icon on the buy screen to jump to the Buy tab in the right place to place a bid (avoiding needing to search it again)

Sorry for my late reply.

You can click on the item's name/icon on the buy screen to jump to the Buy tab

Yes, that's exactly the workaround I'm using 😉

Point of my suggestion was to avoid that, by adding a possibility to bid in Auctionator's Shopping tab. (After all, it's called "Shopping" tab, not "Buyout" tab 😉).

I don't know if it's just on my realm, but there seems to be a noticeable trend towards posting things with really interesting bid prices (I mean something like 20% below buyout, not the usual 1 to 5%). So I find myself switching to the Blizz Buy tab quite often these days.