As it's a Saturday and you are returning the same day there is a modest saving to be had with split tickets using Off Peak Day Returns. (All fares inc. 16-25 discount)
Ashchurch-Bristol TM £4.90 CDR
Bristol TM-Warminster £5.95 CDR
Warminster-Romsey £8.60 CDR
Romsey-Ryde Hoverport £16.00 CDR (£16.70 to Ryde Esplanade)
TOTAL: £35.45 (£36.15 to Ryde Esp.)
Looking at Advance fares for 24th July, there's nothing with a through booking from Ashchurch but you can do the following (prices correct as at 0153 22/06/2010):
Ashchurch-Bristol TM £4.90 CDR
Bristol TM-Portsmouth Harbour £9.55 ADV on the 0823
Portsmouth Harbour to Ryde Esplanade* £10.50 SDR
Portsmouth Harbour to Bristol TM £7.25 ADV on the 1723
TOTAL: £32.20
The 1723 is the last train from Pompey that you can safely catch for a connection to Ashchurch at Bristol at 2000. The later 2041 to Ashchurch is subject to engineering disruption and is planned to be a bus from Cheltenham.
Have a good day out!
*This fare appears on booking engines and in NFM06, so there should be no trouble purchasing it, despite what prd101 said. He's right about the railcard discount though.