I feel your pain living in a new build flat with no outside space…!
I used to wash mine in the bath but not sure it’s all that great for the health of the bike as it’s almost too wet! As my shower has a fixed showerhead water pools in vital areas like the headset and BB, it’s also pretty annoying with the bike falling over without the wheels on. I agree it doesn’t make a mess though, the first time my mrs caught me washing the bike in the bath was an interesting conversation, but testament to the fact I’d washed it several times previously without her noticing…
I’ve made ‘friends’ with the local car wash guys and now just head down with a few quid in hand and they let me have free reign of the facilities from buckets and sponges to the jet washes, its much better than a petrol station jet wash as there is no time limit and you can do a proper job.
Might be worth scouting at your local area to see if you can find somewhere like a car wash place.