Travel from Oxford to Watford Junction without going into central London

Probably the easiest way is to get the X5 bus from Oxford to Cambridge as far as Milton Keynes, and then take the train from there to Watford Junction. Don't know how easy the change in Milton Keynes is, though.

Why do you want to avoid central London?

Yup, the X5. https://www.stagecoachbus.com/promos-and-offers/east/stagecoach-x5 Frequent and comfortable. There is a stop in Milton Keynes directly in front of the Milton Keynes Central rail station, and there is frequent London Midland train service from platforms 1 and 2 to Watford Junction taking as little as 24 minutes or as much as about 40. There are also hourly Southern services from platform 2A or 2.

Very straightforward.

Since you didn't want a train, 208 bus to Aylesbury, 500 bus Aylesbury to Watford. Takes up to 3 hours though.

I missed the bit about not wanting either London nor a train.

The OP asked about a bus or Uber. Although I suppose 'another company' would include trains.

For the fairly short distance all the public transport options are pretty miserable how long they take timewise.

The via London journey is 2+ hours - although I now see the avoiding London part is in the title. Arguably going along the Circle avoids central London ...

Wait for the Varsity Line to return. That will be, so they promise - but who takes a single word from the government seriously anymore - the resurrection of the train line from Oxford via Bletchley (part of Milton Keynes) to Cambridge. Then it would be trivial, Oxford > Bletchley > Watford Junction. But probably not in my lifetime nor that of our childrens' children.

But in the mean-time, the X5 does fairly well.... and its comfy with leather seats and wifi.

The X5 is fairly comfortable (it is a coach really rather than a bus unless you are unfortunate to get a substitute vehicle) but even its best friends would struggle to call it really quick, the main problems being going into and out of congested towns/cities.

There was a time when it appeared in some rail searches but that seems to have gone these days.

The other problem is the road infrastructure. The X5 has to go cross-country, and motorways tend not to do that, so it gets stuck behind the slow traffic too.