Comparing a bus route map for Coventry with Parkopedia's map of all car parks in the city, shows that your plan isn't a particularly easy one to carry out in practice. If it was me, I'd bite the bullet and use the hospital car park. (It's very easy to get to without going anywhere near to the centre of the city, which is one of my least favourite areas in the country to drive around).
If you're determined to give your plan a go though, I offer the following suggestion:
Park on the Clay Lane (surface) car park, which is just off the A4600 Walsgrave Road. (Postcode CV2 4LH. 3 hours = £2, 4 hours [max] = £5). Walk back to Walsgrave Road, turning right at the end of Clay Lane to reach the nearest bus stop (on the right-hand side of the road as you're walking). Take a 9, 9A, 17, 17A, 85A or X6 bus to the hospital from there.