Battle of the bottle!

Have you tried giving him the whole feed before his bath? Do you give him the bottles before or after solids? and do you give bottle and solids at same time or a gap in between? Might be an idea to mix the order around till you find what works best.
It could also just be a stage, i'm having a bit of the same trouble here where he will drink a bit (enough to stop him being starving) and then gets distracted by everything else around him, is especially bad when we are out and he has new stuff to look at.
One good way to get water into him might be to give ice cubes to suck on, I do this with Spencer in his fresh food feeder (but a bit of muslim and elastic band would do the same job).

This is Spencer's rough routine (changes a bit everyday)

6am 180ml bottle straight back to bed
8am get up
9am 180ml bottle then porridge and fruit
Sleep at 11am
1pm 180ml bottle then lunch (3 icecubes worth of meat/veges/fruit)
3.30pm Sleep
5pm 180ml bottle then dinner (3 cubes worth of meat/veges/fruit)
7pm top up usually about 80ml then bed. (sometime he has bath sometimes he doesn't but will have bath then top up)

I usually give him about 10mins between finishing his bottle and having his solids as that has seemed to stop him spilling so much.

With giving the food after the bath i would try giving it to him whilst he is wrapped in the towel and then when he starts to doze off get him dressed which should wake him up a bit and then give him the bottle again.

I would also, if you are worried about him not having enough milk, give the bottles before the solids, if he has eaten and then is offered a bottle only 1-1.5hrs later he may just still be filled up.

I am still breastfeeding Ella, but at the moment I am having a bit of trouble trying to get her to drink enough milk (although it is a bit difficult to tell). What I have found that helps is getting her to feed in a darken room (no toys to distract her) and letting her drink as much as wants at the start of the feed and then 30-40 mins later offering her some more milk (80% of the time she will drink some more). When she goes to her caregiver twice a week, I get her to do the same thing but with the bottle and it does work then as well. I also offer her solids about 1 hr after she had her milk (the first go).

It does get annoying through, when you know that should be hungry and they aren't drinking/eating enough....particularly when they wake up in the middle of the night demanding a feed

So how much is enough liquid for a day?

I think the general rule for fluids is 90-100ml per kg at around 1 year old - I think.
Keep in mind other fluids too, not just formula and water, maybe giving him some cold soup or a bit of juice with the water. Ice cubes or a fruity ice block. Also some fruit & veggies are mostly water like watermelon - maybe try those.
I spoke, about a month or so ago, to Plunket as Gina wasn't much into her water then, and was told that unless bubs is unwell they are not too worried about fluids and that babies will drink when thursty.