I have birds that ADORE getting a bath and I have birds that HATE but I've never had a conure which did not like it. The trick is to try different ways many times each (because, with parrots, it takes seeing or experiencing something many times for it to become familiar and acceptable) without actually forcing them. Start by offering different kinds of bowls in different shapes and different materials, big bowls, small bowls, deep bowls, shallow bowls, metal and plastic and in different colors. Try putting a couple of little pebbles at the bottom (sometimes they are afraid is too deep and seeing the pebbles at the bottom helps with that). Try the mist bottle from above and, if they fly away from it, start by leaving it nearby for a few days, then start carrying it in your hand until they no longer react to it and, when this happens, start spraying a few inches in front of their feet and, as you see that they don't move away, make it closer and closer until you can spray their toes - just once the first time to see how they react and, as they stopped moving away, more times. Then you start moving the spray up very gradually and very slowly until you can spray their entire body. But also try the sink with a small thread of water flowing out of the faucet - and try it falling on the sink and into a shallow bowl to see which one they prefer. Some of them just love water with a passion and would take a bath every which way they can (my cockatoos would even get under the hose stream when I water my garden!). In my personal experience, conures like to bathe in a large bowl with shallow water.
What I always do with all the birds regardless of whether is spray bottle, bowl or garden hose is sing the same song (I sing 'Singing in the rain' - the one and only verse I know which I repeat over and over
). I use this technique with everything I do for and with my birds - I always let them know what is coming, whether is my uncovering their cage ("Good morning!"), opening the door to their cage ("Come out?"), getting their food ("UUUUUUHHHHH, LOOK - LOOK - LOOK! Mmmmmm! Que rica papa! So yummy, so yummy, there's a party in my tummy!"), going out to run an errand ("OK, you be good babies and I see you later! ByeBye, bye-bye, good babies!"), covering their cages or leaving the bird room in the evening (Nite Nite - I love you!). I believe that keeping strict routines and letting them know in advance what is going to happen reduces the stress of captivity as it gives them a feeling of been in control of their own lives (something we take away from them when kept in captivity and which is hard on parrots).
But, of course, all this takes time and you need to provide moisture ASAP so your best bet is a humidifier.