I will try and give an answer from a Vaishnav (Gaudiya) point of view. In Bhagavad Gita 7.16, Sri Krsna tells us that 4 types of people will approach the Lord (in the mood of Bhakti):
catur-vidhā bhajante māḿ
janāḥ su-kṛtino ’rjuna
ārto jijñāsur arthārthī
jñānī ca bharatarṣabha
O best among the Bharatas, four kinds of pious men begin to render devotional service unto Me—the distressed, the desire of wealth, the inquisitive, and he who is searching for knowledge of the Absolute.
As you can see, even those who have selfish desires can perform Bhakti, and get immense pious credits (punya) from the action. In fact, performing Bhakti of the Lord is even more powerful then many normal Punya Karya (like giving charity etc). In Skanda Purana (quoted in Hari Bhakti Vilasa) it is said:
go-koti-danam grahane khagasya
govinda-kirter na samam shatamshaih
"Neither giving millions of cows in charity, nor residing at Prayaga by the Ganges for a kalpa, nor performing millions of yajnas, nor giving a Mount Meru of gold in charity brings a benefit equal to one-hundredth part of the benefit obtained by chanting the holy names of Lord Govinda."
kshetradinam ca yah sthitah
akrishya harina sarvah
sthapita sveshu namasu
"Lord Hari has gathered from charity, vows, austerities, pilgrimages, the demigods, the great saints, the rajasuya and ashvamedha yajnas, and the study of transcendental knowledge all their powers to bring auspiciousness and remove sins, and placed these powers in His holy names."
pratar utthaya yo vishnum
labhate phalam uttamam
"A person who regularly rises early and worships Lord Vishnu attains a pious result better than that obtained by performing a thousand agnishtoma-yajnas.
Shastra is filled with literally hundreds of these statements (especially in Srimad Bhagavatam, which says that Bhakti can easily grant Mukti, what to speak of artha, kama etc). Srila Sanatana Goswami has compiled a list of various verses from Scripture confirming this in the 11th Chapter of Hari Bhakti Vilasa .
Srimad Bhagavatam says:
*na niskrtair uditair brahma-vadibhis
tatha visuddhyaty aghavan vratadibhih
yatha harer nama-padair udahrtais
tad uttamasloka-gunopalambhakam *
"By following the Vedic ritualistic ceremonies or undergoing atonement, sinful men do not become as purified as by chanting once the holy name of Lord Hari. although ritualistic atonement may free one from sinful reactions, it does not awaken devotional service, unlike the chanting of the Lord's names, which reminds one of the Lord. Bhag. 6.2.11
You can also read in Srimad Bhagavatam, the story of Ajamila, who out of selfish reasons called out "Narayana" at the time of his death, yet attained Mukti.
However, when such Bhakti is done for selfish reasons (i.e for Bhukti or pleasure of body) then such Bhakti is called Karma-Mishra Bhakti (Bhakti that is contaminated with Karmic activity). Similarly, when Bhakti is performed with the desire for liberation, it is called Jnana Mishra Bhakti. Bhakti reaches its purest form (called Suddha Bhakti) when it is performed out of no other desire than to please the senses of the Lord. Such Bhakti can be called "selfless". Srila Rupa Goswami writes in his Bhaktirasamrta Sindhu the following definition of Bhakti:
anukulyena krsnanusilanam bhaktir-uttama
"Perpetual, ardent endeavor meant exclusively for Sri Krsna and performed out of genuine kindness* to Him, when neither prone to any selfish, ulterior desires nor eclipsed by impersonal knowledge, fruitive work, or any other occupation, is known as uttama-bhakti (highest Bhakti)"-Sri Bhakti-rasamrta-sindhu (1.1.11)
So in conclusion, selfishness in Bhakti does give immense pious credit (punya) and even Mukti, but these are simply fractions of the power of Bhakti. The true fruit of Bhakti (and Nama Sankirtan) is the manifestation of Bhagavata Prema (Love for God) which is intrinsically selfless and causeless for it is the eternal nature of the soul. This mood is encapsulated so beautifully by Bhagavan Chaitanya Mahaprabhu in the 4rd Shloka of His Sikshastakam:
na dhanam na janam na sundarim
kavitam va jagad-isha kamaye
mama janmani janmanishvare
bhavatad bhaktir ahaituki twayi
O almighty Lord, I have no desire to accumulate wealth, nor do I desire beautiful women, nor do I want any number of followers. I only want Your causeless devotional service birth after birth.
I hope this helped,