A At 4 months, thumb sucking is not a bad habit -- in fact, it's the opposite -- and there's no need to try to stop your daughter from doing it.
As you may know, babies are born with a sucking reflex. Your daughter's capacity to bring her hand to her mouth is a product of the Babkin reflex, which can even be seen in utero. I know many new mothers who first saw their thumb-sucking baby through the grainy haze of a sonogram in their obstetrician's office.
Some babies have a stronger need to suck than others -- like all areas of infant development, there is wide variation in what is normal. Just because your friend's baby doesn't take a pacifier or suck her thumb, or just because your neighbor managed to stop her baby from sucking her thumb by using mittens, that doesn't mean your little one will be the same, and you should not expect her to be.
The importance of sucking for infant self-soothing has been demonstrated in a variety of studies. For example, pacifier use or thumb sucking is often offered as a way for babies to tolerate the pain of needle punctures or other painful medical procedures. Nonnutritive sucking has been found to help the development of preterm babies, and in all babies, thumb or pacifier sucking is associated with self-calming. Thumb sucking may increase when your baby is tired or unhappy, as well as when she is unwell or teething. The thumb, therefore, provides your baby with a way of calming herself down -- providing her with important experience in managing her emotions. In addition, a baby who is not distressed can then devote her energies to exploration, to eating, and to the many other challenges of development.
Research also suggests that thumb sucking that stops by the age of 2 will have little to no effect on growing teeth. Some studies indicate that any tooth misalignment that occurs among children who suck their thumb for even longer will self-correct if it discontinues by 5 years of age or so.
If you're worried that your baby will become "addicted" to her thumb, you may have a legitimate concern. But most children stop by the time they finish the toddler years, and one researcher suggests that more than half stop by 7 months. So there is good reason to believe that your daughter will stop on her own eventually. Some children stop sucking during the day, but nighttime habits linger for a little longer; this also wanes with time or, if necessary, with interventions like the awful-tasting liquids you may have seen in stores, which are not to be used on children of this young age.
You can also find a compromise between total indulgence of the habit and complete prohibition. For example, you can let her suck her thumb to soothe herself when she's cranky, but once she has calmed down (if she's not asleep), you can offer her some exciting toys so that she's motivated to use her hands for other purposes. If she falls asleep with her thumb in her mouth, you can try to remove it so that she doesn't become accustomed to sleeping that way. Such methods can help thumb sucking become just one aspect of a repertoire of self-soothing skills.