Have you considered a wood look vinyl plank flooring? Most probably can be laid directly over the 'linoleum' (vinyl sheet flooring or real linoleum)? With the vinyl plank, you will have minimal height differences between it and adjacent flooring.

Pretty sure that would void your flooring warranty.

I'm with O&B. I HATE the 'screw down' plywood concept. The idea behind a vapour barrier is to stop water intrusion coming UP from the ground. As soon as you pierce the concrete (with or without roll on vapour barrier) you create a hole where water can escape through.

If you are going to leave the 'lino' (probably sheet vinyl? or are we talking tiles?) then you might as well float the wood floor. For that you will still need ++++slab preparation (carpets hide the WORST subfloors in the WORLD...so FYI you will want to be prepared to pay ++ for prep) AND vapour barrier (roll on = expensive; sheet vapour barrier = silly-cheap!).

If you float your wood floor, you can use 1/4" cork underlayment to make the wood floor feel solid under foot and remove the 'bounce' of a floating floor.

Remember: your expensive floor is only as good as the subfloor it is sitting on. If you muck up the subfloor you muck up the ENTIRE expensive flooring product.

Thanks for the feedback. The linoleum is tiles. I really wanted to do solid wood nail down bamboo but that's sounding like its not going to work. Would it be better to put down an AirGuard underlayment and float an engineered floor over that? I want to do it right and still be cost effective. It's just that there are so many options out there.

The wood flooring manufacturer may be the one to determine the underlay (this is rare but it has happened). Be aware that bamboo is NOT wood. It is 30% adhesive (aka 'binder'). And it is very difficult to live with (needs SUPERIOR humidity control from a SUPERIOR HVAC system with humidistat upgrade).

You will need to bring in a flooring professional to tell you how to deal with the substrate. S/he won't be able to do that until all of the existing flooring has been removed and the full state of the concrete slab.

If, your slab is flat. You can float 2 layers of 1/2" cdx panels over 6mm plastic and nail onto the panels. Use Aquabar or a roll-on moisture retarder. You would need to check for clearance with doors and stairs.

If, your basement humidity stays between 40-50% . Bamboo will perform fine.

It is a first floor bedroom not a basement. The issue with 2 layers of 1/2"cdx and then the wood flooring is that it would put the total floor in the bedroom way above the rest of the 1st floor of my house. The rest of the house is hardwoods. Right now I have about 7/8" between the concrete floor (currently covered with linoleum) to the top of the existing hardwoods.

Thanks for all the input. The more I go around with this I think come back to floating an engineered product like this

https://www.homedepot.com/p/Home-Decorators-Collection-Strand-Woven-Distressed-Dark-Honey-1-2-in-T-x-Multi-Width-x-72-in-L-Engineered-Click-Bamboo-Flooring-HD13004A/205112454

Or is that just a really bad idea?

Bamboo is a tricky duck. It requires HIGH END production to get the 'cast iron' finish people claim it to have. A high-end product starts around $10/sf and moves (quickly) into the $15/sf range. The link you showed is $2.70/sf.

If you MUST float a bamboo floor (or any solid wood-like product) please use the 'glue edge' approach. And please work with something in the 3/4" range. And please work with something CERTIFIED as 'old growth bamboo' (which is classified as grass poles 9 years or older).

I can pretty much guarantee the $2.69/sf click together bamboo is not going to give you the easy life nor the 'cast iron' wear touted by bamboo lovers. Bamboo lovers will have purchased the $12 - $15/sf stuff that is solid strand old growth product in a natural colour. And it was probably installed with a glue down system (the really tough bamboo is horrible to puncture with a nail or staple gun!).

If $3/sf is your budget and you are looking at a click together floor, you can purchase a VERY VERY nice laminate for that range. As in 'European Grade' product with off-gassing that is LESS than a jar of pickles!