detergent always leaves a very thin film behind, which will definitely effect your adhesion.

Alcohol or acetone will remove any organics (things with carbon based molecules) and totally evaporate, leaving a much cleaner and 'stickier' surface.

It does depend on what the print bed is made of whether you use acetone or ipa.

I mean all you need to do is to get a folded sheet of kitchen paper. Briefly upend the bottle so it dampens the paper. And give the bed a quick wipe.
It's so quick that the chances of it effecting even something soluble is minimal.

And you don't need to clean it very often.

In your case.
I'd wipe first with a water dampened sheet - to remove the residual detergent.
Then an alcohol wipe to remove any residual grease.

The little packets of glasses wipes or computer screen wipes are usually ipa. they work well and you can get them from buckstores/poundstores

And then physically level the bed.
Remove filament and heat the nozzle to 200c Before starting the level.

Always level with a cold bed and a hot nozzle.

I have tried heating both - but I've always had the best results with just a heated nozzle,
:-)