Hi Mellyboots,
I'm also a non-driver (located in Birmingham) .There are many excellent places that you can get to from Worcester which are excellent for butterfly watching.
The top spot at this time of year I would say is the Wyre Forest (train to Kidderminster followed by bus to Buttonoak). See my trip report under "personal diaries" for comments.
There's a bus which takes you east to Grafton which is well known for its Brown Hairstreaks later in the year - this species is present all the way from Worcester to Redditch.
Further afield, Oxford is pretty interesting (Black Hairstreak), and you might be able to get a bus to the Bredon Hill or Broadstairs areas. Both of these are recommended in summer.
You are probably familiar with Perry Wood and Nunnery Wood which have White Letter and Purple Hairstreaks reported, although I have not seen these in Worcester personally.
I'm sure there are many butterflies waiting around in forgotten corners of Worcestershire for you - keep us posted with what you find!
Alexander