I don't have a puncture repair kit nor levers to open the tire.
You'd be well advised to get them and learn how to use them, as punctures are an inevitable part of cycling. It's not a difficult job.
Plus I'm not even sure how to correctly clean a bike.
People make more of it than it really is.
A bucket of soapy water and a brush will do for non greasy bits, but your chain and gears will last longer if you clean those occasionally too. For the gears a brush with some solvent, degreaser or chain cleaner is better than nothing, but you can do a better job of it if you remove the chain. People have various favourite tools for getting into awkward places.
What I'm fearful of, is removing lubrication from bearings
The rain will do that for you. You will need to re-lubricate the transmission if you clean it, and occasionally if you don't. Cleaning gears is easy because they're exposed, but other bearings are not that difficult, there are plenty of videos on You Tube to show you how. Bearings that need occasional attention are wheel, pedal, steering and bottom bracket, along with cables, brakes and gear change linkages, but nowhere near as often as the gears.
I'm lucky the tire didn't deflate while riding. I would have had to walk 7 miles home with the bike in the rain, totally drenched in the cold.
It'll happen sooner or later if you aren't able to deal with punctures yourself. (That said, Anne Mustoe cycled round the world unable to mend punctures, but I wouldn't count on being as unbelievably lucky as her.)