Mulching helps to conserve soil moisture and suppress weeds but keep mulching material away from plant stems. Feed annually in spring with a balanced fertilizer such as blood and bone at a handful per square metre in spring as new growth begins. Make sure the plant gets ample water throughout dry periods. A good rule of thumb is to give your roses one deep watering each week in dry times. This will ensure the roots look for water themselves. Check ties for chafing and constriction and loosen if required as the plant grows.
As for feeding your roses, most varieties will do very well with a single feeding in early spring when the leaves start to bud. Since Dublin Bay roses are repeat bloomers, you can feed them several times through the growing season to encourage additional blooms. Give a second feeding just as the first big bloom starts to develop and one more in the middle of the summer to promote later flushes. Use a quality fertiliser (preferably organic) which contains a balance of major nutrients (NPK) and trace elements. The fertiliser should be applied at least once a month or a small amount often with fortnightly applications of liquid seaweed over the foliage.
Pruning climbing roses is pretty easy and for the most part you are pruning for health and shape. Prune in June or July while the plants are dormant before the leaves open up as it will make it much easier to see what you are doing. 70% of the rose plant should be pruned. Always start off by removing the dead wood, along with any canes that look diseased, any very old wood can be removed back to the crown, and the bush pruned to shape. Cut back any lateral canes that overlap one another. Once the leaves open up these overlapping canes will compete with one another for sunlight. Also, cut back any canes that are growing beyond where you want and train the remaining canes to whatever support you are using. Shape the rose to whatever general shape you desire.
Take the opportunity to also rake up dead leaves and debris from around the base of the plant as these can lead to pests and diseases re-infecting your plant for the following season.
Deadhead regularly throughout the flowering period to help encourage more blooms.