BabyBinkCotwell(AdamRobertWortonandJacobJosephWorton),themainprotagonisthasadoringparents,livesinahugemansion,andisjustabouttoappearinthesocialpagesofthepaper.Threeklutzy,would-bekidnappers:Edgar"Eddie"Mauser(JoeMantegna),Norbert"Norby"LeBlaw(JoePantoliano),andVictor"Veeko"Riley(BrianHaley),themainantagonists,disguisethemselvesasthephotographersfromthenewspaperandkidnapBabyBink.AfterthekidnappingEddie,Veeko,andNorbyhavedifficultycontrollingBink.InthetrialoftryingtogetBinktofallasleepNorbyfallsasleepreadingBink'sbook,leavinghimunattended.LookingthroughhisbookBinknoticesabirdonthepageandthenbythewindow.Binkfollowsthebirdoutthewindowandsuccessfullygetsawayfromhiskidnappersoneofwhom(Eddie)fallsoffthebuildingintoanalley.

　　NowoutsideonthegroundandcrawlingaboutBinkfindsanotherpartofhisstorybook,thebluebus,whichhethenboards.ThekidnappersrealizeBinkismissingandstartchasingthebusintheirvan-theireffortsareinvain.MeanwhileonthebusBinkcrawlsintothebagofanobeseladywholeavesthebusatherstopshortlyafterwards.Bythetimethetriocatchesthebus,andrealizeBinkisnotonboard,thetriothanrealizesthatBinkhascrawledintothelady'sbagandfollowher.Analtercationensuesafterthekidnappersinsultthewoman,andwhilethethreeattempttheirescape,Binkcrawlsuptoarevolvingdoorattheentrancetoamallandisforcedinwardsbythedoor'smomentum.

　　Crawlingthroughthemall,Binkisstoppedbyateenagerwhoworksforanearbydaycarecentre,whobelievesheisanotherbabywhoescapedfromthecentre.Binklaterescapesthedaycarecentreandthemallandeventuallycrawlsintotraffic.ThekidnappersattempttofollowhimbutkeepgettinginjuredintheprocessasBinkmakeshiswaytoanearbyzoo.Theyfindhimintheprimatehousewithagorillaandlosehopeofgainingtheirransommoney.Thegorillashowsamaternalsideanddoesnotinjurethebaby.ThekidnapperstrytoretrievehimbystickingabroomhandlethroughhisoverallsstrapsandliftinghimupoffthegroundbutthegorillanoticesandgrabsBinkbyhisoverallsstraps.Itthenusesthebroomasacatapultandsendsthekidnappersflyingawaywithoutthebaby.

　　ThekidnapperseventuallycornerandcatchBinkinapark,butareconfrontedbytwofriendlypoliceofficers,whohavespottedtheirvan'sengineisstillrunning.Duringtheconversation,EddiehidesBinkunderhiscoatinhislap,butBinkreachesEddie'slighter,setshiscrotchonfireandsneaksoffassoonastheofficersaregone.VeekoextinguishesthefirebystompingrepeatedlyonEddie'sgroin.TheyfollowBinktoaconstructionyard,butarestillunabletocatchhim,eachofthemendinguptrapped.ThesunsetsasBinkleavestheconstructionyard.Thekidnappersmanagetoescape,butdecidetogiveupandgohome.

　　Bink'sfamilyisnotifiedofvarioussightingsoftheirbabyinthecityandtheirnannydeducesthatBinkhasbeenfollowinghisfavoritestorybook,"Baby'sDayOut"(or"Boo-Boo",asBinkcallsit)andwillmostlikelyheadfortheOldSoldiers'Homenext.Sureenough,theyfindBinkthere,butonthewayhome,Binkbeginstocallout"Boo-Boo"towardsthekidnappers'flat.TheFBImovesinontheflatandarrestsEddie,VeekoandNorby,demandingthattheyreturnBink'sbookfirst.

　　Backhome,Binkisputtobedbyhisfamily.Ashisparentsdiscusshaving