The council is proposing to move the service to community space at Marigold House, the new care home being built at the former police station site, Hockliffe Road, while the existing Duncombe Drive centre would close.
It is now seeking residents' thoughts on the relocation, which can be given via an online questionnaire, email or letter, but is keen to emphasise that the new location would be "dementia friendly" and more cost-efficient.
CBC states: "The council believes it can offer better opportunities to Leighton Buzzard Day Centre customers and is therefore restarting the consultation.
"We have arranged face to face meetings with the customers of the centre and their families, so they can talk to us and have their say."
A 12-week consultation on the future of the centre was launched before the pandemic, but due to Covid-19 the services - and research - were temporarily suspended.
Although home visits were provided instead, last summer there were calls for the centre to reopen, as residents began to fear for its future, and claimed that the "one thing people had been clutching on to" was the hope of returning.
The centre caters for elderly residents, as well as a Community Opportunities Group (COG) for people with learning disabilities, and finally opened its doors on March 14.
However, it is not yet known where the latter would be relocated, as CBC states: "If the Leighton Buzzard Day Centre were to close, then an alternative ‘touch down’ base would be required for the COG.
"During the consultation period the council would continue to work with the COG customers to identify what they would like to do and where they could run activities from if the preferred option is approved."
CBC also noted that it was "committed" to keeping COG running in Leighton Buzzard.
Meanwhile, it is thought that elderly residents would benefit from an "improved setting" and increased social interaction at Marigold House.
CBC states: "It would enable existing customers to access more modern facilities and a comfortable dementia-friendly environment, with access to secure landscaped gardens."
It also states that the the group would be able to stay together and that the move would see running costs reduced.
It added: "By co-locating both the care home and the day centre, both services can run more efficiently and effectively."
As well as relocation, a number of options were considered by the council, including refurbishing the current centre, commissioning a new provider, moving customers to other CBC day centres, and 'doing nothing'.
However, it was felt that relocation to Marigold House was best in terms of improving facilities and services, minimising disruption, value for money, and meeting key principles.
Please visit the CBC website for more information and to complete the online questionnaire.
You can also email your thoughts to: [email protected] or write to: CBC at FREEPOST RSJS GBBZ SRZT (you do not need a stamp), MANOP Team, Leighton Buzzard Day Centre Consultation, Central Bedfordshire Council, Priory House, Monks Walk, Chicksands, Shefford, SG17 5TQ. The consultation closes on July 7.