My lovebird Kia used to bath the same way as Abby's bird. Now he to sit on an upside down stoneware plate in our kitchen sink while i shower him with warm water (we have a spray attachment to rinse dishes). My other lovebird Chicken prefers to be misted with warm water while in her cage.

 

I would suggest trying the misting because they aren't tame yet. just make sure that if you are doing it while they are in the cage, dry off perches & bars afterwards.

 

sometimes just a plain flat / shallow earthenware dish at the bottom of the cage with nice warm water will coax them into bathing.

 

as long as your house is warm and the water is warm they shouldn't catch a chill.

 

good luck.

....My little LB, Misty, used to love the tap water as well.  She never used the bath I got her...so that went by the wayside and the bathroom sink became her shower!

my lovebird wont go in her bath unless i do this:

 

put the bath in the bottom of the cage full of water

take a cup full of water and dip your fingers in it so they get wet

then gently "flick" water droplets onto your lovie's feathers

this coxes my lovie straight into the bath and she loves the misting action!

you can also try a gently spray bottle!

also make sure your bathtub water isnt to cold or to hot!

hope this helps!

happy bathing!