Bishop warned that the ODA's decision to hold only one design-led competition - for the Carpenter's Lock footbridge on the River Lee waterway - and to rely on a 'one-bridge-fits-all' strategy for the remaining 31 bridges would have serious ramifications.
Bishop said: 'The Olympics is also about providing something amazing for London - a legacy for the future - and you can't separate out the design for bridges. You can't divorce that from the overall design strategy of the park.
'We must not be left with something that constrains us unnecessarily. A bridge should be a beautiful, joyful structure in the park and it is important we don't lose that opportunity,' he added.
Aside from the Carpenter's Lock bridge, the park's 13 remaining footbridges, five land bridges and 14 road bridges have been lumped together in seven lots according to function and geography.
Referring to those lots, an ODA spokesman defended the decision to use a single design. He said: 'Each bridge will be designed on its own merits and worked up by the team that wins each lot.
'But it is fair to say that the design of the park's infrastructure will be by a construction-led consortium. The logistics of having design competitions for 30-plus bridges is just not feasible,' he added.
The attack by Bishop - who has the final say on all design decisions taken by the London Development Agency and Transport for London - on the ODA's single-bridge policy adds considerable weight to concerns expressed by CABE at a design review last month.
The quango issued a lukewarm response to the Arup design and said: 'There is a case for extending the scale parameters that limit the bridges to flat structures to allow for a vertical expression of the design.'
Bishop was unconvinced by the ODA's assertion that the Carpenter's Lock footbridge 'underlined [its] commitment to design and innovation'.
'It is never acceptable that time constraints should preclude design,' he added.