Why didn't Saruman go to the Shire to take the Ring?

[HerenIstarion]

Most likely Saruman hopes that Gandalf will come bringing the Ring with him

Seems to me you've answered your own question well enough putting forth quote as above

Another reason may have been psychology - Saruman has grown used to being the Lord of Orthank with all the benefits and comforts it brought along, being even afraid to an extent of venturing abroad alone (as opposed to Gandalf who's wandering about on his own most of the time). (cf. his heavy stress on 'destruction of his home' encountering the returning Lords of the West in Hollin and also remark made in conversation in Flotsam and Jetsam I believe about faded wizardry of Saruman's who has to rely on 'wheels and chains and slaves' now)

It seems the mark of all beings going evil that they exhibit less courage the more evil they become (cf. Morgoth and his self-imposed confinement towards the end) and less will/capacity to independent action - you can tell the one has started going rotten as soon as they start to lean towards Denethor's wisdom (good captain sitting back sending forth his inferiors)