The 24,000 households served by a transmitter at Bathampton will only be able to get the five terrestrial stations and around 10 others if they buy a Freeview digital box to cope with the analogue switch-off which begins on March 24.
Other parts of the area which get their signal direct from the Mendip main transmitter in Somerset will get around 40 channels in total.
The locations likely to receive the reduced service include Oldfield Park, Southdown, Larkhall, Fairfield Park and parts of Twerton, the city centre, Batheaston, Bathford and Bathwick.
In order to get a fuller service, rather than buy a digibox costing as little as £25, they would have to pay £175 for the Freesat From Sky service, which offers around 240 channels, or £59 for a box and around £80 for a dish for the basic Freesat service with more than 140 channels.
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The alternative is to sign up for a subscription service such as Sky, Virgin Media, or BT Vision.
At the moment, many homes in Bath cannot get Freeview at all but after the switchover, they will be able to receive Freeview for the first time, seeing the number of channels available through an aerial increase.
Anyone who has not converted their TV to digital after switchover will be faced with a blank screen.
It is not known how many homes have already bypassed the Bath relay transmitter at Bathampton by switching to satellite or cable providers already.
The litmus test of which transmitter you are served by is whether you can currently get Channel Five terrestrially – if you cannot, you are served by the Bathampton mast.
The channels likely to be received from the Bath relay station are BBC1, 2, 3 and 4, BBC News and BBC Parliament, CBBC and Cbeebies, ITV 1 and 2, Channel 4, E4, More4 and Five.
The digital switchover will begin on March 24, when BBC2's analogue service is switched off, and be completed on April 7 with the rest of the terrestrial channels.
Some viewers have described the transmitter system as unfair as the two relay stations serving Bristol are geared up to provide all 40 channels.
TV firm Moss of Bath has been organising information sessions at its store on the switchover.
Spokeswoman Annie Moss said: "The response has been incredible. They've been very well attended – it's just such an eye-opener, there's so much confusion out there and a lot of misinformation."
The city centre firm was inundated with inquiries when there was a national retuning exercise in September and is expecting to be busy again in March and April.
It is offering free advice on the phone but many people paid a call-out fee for staff to go to their homes to sort out problems.
City MP Don Foster said the two-tier system in the city was not going to be solved by political pressure and was purely down to the commercial decisions of TV firms not to pay for the technology needed at relay stations.
Mr Foster, who is the Liberal Democrat party's culture and media spokesman, said: "It's absolutely critical that people who have not yet prepared themselves are talking to local dealers about the options open to them."
Moss of Bath is hosting its next Digital Switchover talk next Thursday at 10am. Places are limited so early booking is advised, and refreshments will be served.
To book a place, email sales@mossofbath.co.uk or call 01225 331441.
More information is on the website www.digitaluk.co.uk, and by ringing 08456 50 50 50.
