Wachau Valley from Vienna: Need advice on biking from Melk to Krems, or Krems to Melk

This company lets you reserve bike pick up in Melk and return in Krems. Decent quality, reasonably maintained bikes:

https://wachaubike.at/

You'll need to translate the website.

The public pay-share bikes Nextbike are also available, and you can drop them off at any Nextbike station with capacity. If they are all gone (unlikely) you are SOL, and they are cruddy bikes not wholly reliable for the 40-50km trip you want to take.

It's a very pretty ride on either side of the river. You can stay on the Melk (south) side of the river or safely cross right away to the north side on the bridge at Melk. Otherwise if you head down the south side of the Danube from Melk you'll need to use a ferry if you want to cross over to see Durnstein - so maybe wait in line if it is busy. I'd cross to the north side right away at Melk.

The Melk bridge is a highway bridge with a completely separate bike area. It's quite safe. Be aware that it is a bit high on the Melk side of the bridge, so from Melk you need to ride up to it, so short but steep hills to start. Get off and push if need be - the hill isn't long! After that the whole ride is essentially flat.

As for wine tasting, Austria does heurige much more than tasting rooms, and heurige are by far the more cultural experience. There's a cluster of good ones just as you come into Krems. This is because Krems is the wine business hub of the area, so much of the region's wine is made nearby. The heurige are on a single street mostly (Steiner Kellergasse) that rises a bit above the river for nice views. I liked all three we visited on two separate trips. Pichler had the best wine and was very nice:

https://www.pichler-weingut.at/

All in all cycling the Danube through the Wachau Valley is lovely, probably my favorite river cycling segment in all of Europe. Great choice, will be a grand day out.

I couldn't find a direct train from Vienna to Melk

Direct trains from Vienna to Melk depart hourly from Wien Westbahnhof (western train station), always 18 minutes past the full hour, e.g. 8:18am, 9:18am, and so on. The train designation is CJX5, departing from patform 3 in most cases.

I also am thinking that you might not be looking at the correct website. Always use the websites of the actual train companies - in this case OeBB. Here's the link - https://www.oebb.at/en/. I put in some dummy dates for travel from Vienna to Melk and easily saw the direct train mentioned above.