Hmm.
There's a cycle path that follows the ring-road round to the traffic lights by UWE (cut-through to Parkway), but if you take the Sustrans cycle path route from the centre to the ring road you go a fair distance east. There will be a few routes out to the ring road that are more northerly - Parkway is North North-East of the centre.
Working backwards from Parkway, there's a path between UWE and MOD Abbey Wood that goes to Broom hill (you go through the grounds of the big yellow building on a hill you can see from the M32), and you can then get through Stapleton and Eastville into the centre, but afraid to say I've never gone that way - I sometimes ride from Airbus and Rolls-Royce in Filton back to Bath, so start in the environs of Parkway but I turn off by Broom Hill to go out east on the Bath-Bristol cycle track. There's a path that I think goes from the very bottom of Broom Hill down into Eastville, I see a fair few riders dive off down there so assume you can get through. Google sat view suggests it's mostly paths through fields, which bodes well.
(eta: bear in mind it's all uphill, and starts to get quite steep in places from Broom Hill up to UWE)