Hi Michael,
It's great to know you'll be spending time in Wicklow next month; I hope you have a lovely and peaceful time.
Cycling is a fine idea, and bicycle rental is possible in the area.
Biking.ie has an office in County Wicklow; in Ballinastoe, which is quite close to Glendalough, although it only seems to be open on Saturdays and Sundays (as well as bank holidays). Perhaps this would still be an option for you.
Another option, if you wish to explore the south of Ireland, would be to travel to another city and rent a bicycle there. For example, there are a number of options for renting a bicycle in Cork City, such as
Cork Bike Hire. They also have locations in Midleton and Youghal.
I hope this information will be helpful to you.
Regards,
Eoin