Even for more shy and nervous pet birds, with continued training and lots of patience and perseverance it's possible to at the very least finger tame them.
It would be good to work on making Twinkle more trusting and comfortable around you and this can be achieved by spending time close to her cage, getting Twinkle used to your presence, she needs to realize you are not a threat and aren't there to harm her. In order to make a better connection, you can use your voice and talk to her in a calm, positive, encouraging and reassuring way. For the detailed information, check the stickies at the Taming and Bonding section of Talk Budgies.
When cleaning the cage and changing the food/water bowls, it's best to avoid sudden movement with your arms/hands and act as if you are on slow motion.
In order to make the cage cleaning less stressful, you can also have some music on. You can use your voice as well to communicate with Twinkle while you are cleaning the cage.
Later on, you can slowly rearrange the perches/accessories on Twinkle's cage in order to prevent the poop build-up from falling into a particular toy/object.
Do you have a swing on your Twinkle's cage? If not, then it would be good to get her one and attach it to the cage's ceiling.
Most budgies choose their swings as the favourite place to sleep in for the night as that's the place they feel the safest in.
Best of luck with your Twinkle!