Also might help if you say how high the fence is. Depending on the type of roses you choose (as Perki said consider size) you also need to consider good strong trellis or wires to train them horizontally. If it is a weak fence or posts bear in mind roses can be very heavy and need strong supports to train them on.
There are a few nice repeat flowering rambling roses that do not get too huge compared to some varieties. Have you also considered your aspect, which way the fence faces.
Thank you both for taking the time to respond. The fence is 6 feet high (7 panels) and mostly has 1ft of trellis on the top, but lower down the garden it has 2 feet of trellis. It faces southwest and is about 2 years old so quite strong. The fence and bed go alongside a ramp for my husband's wheelchair. So I need to be able to keep the bottom of the roses bare until it gets past his shoulder height whilst sitting. Then I will need to tie them in horizontally. Previously we inherited honeysuckle and other shrubs that needed to be hacked back every couple of months. I have been given a gift of 100 mixed allium bulbs that I thought might go in as ground cover. I don't know enough about roses to make informed choices but I know that I would like them to be medium to strong colour pinks (not keen on wishy washy) or whites.
The fence and bed go alongside a ramp for my husband's wheelchair. So I need to be able to keep the bottom of the roses bare until it gets past his shoulder height whilst sitting. Then I will need to tie them in horizontally.
How wide is the border? Are you sure you want roses there? Some varieties can be trained flatter than others (less than 1ft depth), so if your border isn't too narrow, I would say choose those varieties and train horizontally/to a fan shape from the beginning, removing all canes growing in the wrong direction. If you can't do this because the border is too narrow, maybe it isn't suitable for roses at all. You could also use clematis, for less thorny coverage of the fence. You could alternate clematis and roses if you want. Allium really isn't a good ground cover, its foliage looks ugly most of the time and die back very soon. I would plant spreading geraniums or some other easy perennial, again depending on the width of your border. Two roses I would recommend: 'The Albrighton Rambler' - can be trained very flat, has flexible canes, is low-thorn, relatively small and manageable. 'Malvern Hills' - This is a much bigger rose with very flexible canes, you could keep one or two canes closer to the ground and train the majority of it up and to the sides, on your trellis, and underplant with whatever you like, it goes very well with purple.
This is a bit of a tricky one because, like others, I suspect you might struggle with a rose in that position, especially if you are already having to chop back something like Lonicera. One plant that comes to my mind is Trachelospermum asiaticum. It has scented flowers, is evergreen, and can be shaped and clipped like a hedge almost. It will not get rampant at you and is easy to control with an annual clip, though you have to give it a few years to fill in its support. It is also largely self-clinging, though appreciates a bit of help.
I can sympathise though if your heart is set on roses. In that case I would suggest a thornless variety such as ‘Mortimer Sackler’, just in case.
On the question of ground cover, there’s nothing to stop you using a low, evergreen groundcover like Geranium macrorrhizum at the base of your rose, or Bergenia for example, then having the Alliums do their thing through it. Or if the Alliums are taller then put them among some trouble-free medium-sized (at the time the Alliums flower!) perennial. If it’s quite a narrow bed, as it sounds, then you probably don’t want to go hog-wild with large perennials either, but go for something that stays within its bounds like a good plant.
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Depending on the type of roses you choose (as Perki said consider size) you also need to consider good strong trellis or wires to train them horizontally.
If it is a weak fence or posts bear in mind roses can be very heavy and need strong supports to train them on.
There are a few nice repeat flowering rambling roses that do not get too huge compared to some varieties.
Have you also considered your aspect, which way the fence faces.
Some varieties can be trained flatter than others (less than 1ft depth), so if your border isn't too narrow, I would say choose those varieties and train horizontally/to a fan shape from the beginning, removing all canes growing in the wrong direction. If you can't do this because the border is too narrow, maybe it isn't suitable for roses at all.
You could also use clematis, for less thorny coverage of the fence. You could alternate clematis and roses if you want.
Allium really isn't a good ground cover, its foliage looks ugly most of the time and die back very soon. I would plant spreading geraniums or some other easy perennial, again depending on the width of your border.
Two roses I would recommend:
'The Albrighton Rambler' - can be trained very flat, has flexible canes, is low-thorn, relatively small and manageable.
'Malvern Hills' - This is a much bigger rose with very flexible canes, you could keep one or two canes closer to the ground and train the majority of it up and to the sides, on your trellis, and underplant with whatever you like, it goes very well with purple.