I'm signed up for the auto re-charge thingy - once your card has under £5 it adds £40 the next
time you go to a tube station.

My balance is very low, and I'm unlikely to use the tube this week but will need to use buses. If
I go to the tube station and put my Oyster on a gate (to recharge it) but don't travel, surely
that will result in an unresolved journey? Or can I 'charge' it on the big ticket machine, or ask
at the ticket window?

You can go into negative balance on the bus and your card will auto top-up
when you next use the tube. Ask Oyster doesn't say by how much you can go
below £0. https://transportforlondon.custhelp.com/

You cannot auto top-up by presenting your card at the ticket machine or
by touching-in without travelling (well you can if you like but it will cost you
for the unresolved journey). If you don't like the idea of having a negative
balance add some money "manually" to your card at the ticket machine.