Embassy says the double-decker is currently among a fleet used by stars including Jools Holland and indie rock band Kaiser Chiefs.
Founder, Sid Williams told Premier the vehicle requires minimal adjustments and will help relieve pressure on existing shelters in the city.
He explained: "It's not a regular Routemaster... it's purpose built; it already has 14 beds, two lounges, a kitchen, a toilet and loads of storage."
Funds totalling £30,000 have been secure the purchase - but Embassy says continued fundraising will be required to meet the service's £100,000-per-year running costs.
Mr Williams continued: "Although there are a few shelters, there's a huge disparity between the number of beds available and people sleeping rough.
"Everybody [homeless services] was saying to me, 'If you could provide more emergency accommodation, that would help us in our job of getting people off the street."
The homeless shelter, which is intended to be fully-operational by this winter, will accept clients all year round via referrals from councils and other local agencies.
Describing how the Christian ethos of the charity will be reflected in the ministry of the bus, Mr Williams added: "It starts with rest but, also, it's building relationships [and] connecting people to jobs.
"We're going to be staffed by Christians and Christian volunteers.
"We know that Jesus transforms lives and brings a new level of hope.
"We went to connect people to community in churches."
Half of the projects' upfront costs for the vehicle's purchase were met by property and regeneration specialists Capital & Centric.
Co-founder, Tim Heatley said: "The bus will become a lifeline for those in the city that need rest, support and a route back into a community that cares."
Click here to listen to Premier's Alex Williams speaking with Sid Williams:
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