After all green growth on your bulbs has completely disappeared, you can spray the weeds and grass with glyphosate. I say glyphosate deliberately rather than Round Up - Round Up contains other ingredients which make it more dangerous in the environment, but you can buy a bottle of neat glyphosate from somewhere like Wilkos fairly cheaply, and mix it yourself, adding a little squirt of washing up liquid to the mixture. Works out much cheaper and is less likely to harm other life forms, including you.
However, that doesn't mean the grass won't be back, you may need to carry out more treatments during the summer and the year after to get rid of it. In the situation pictured in your photo, it's possible you have couch grass with roots under that wall, which is probably why digging it out has been unsuccessful - you can't get at those roots and it just spreads back out. Glyphosate works 'through the green' so to speak - the more strongly the plant is growing (grass, in this case), the more effective the treatment will be, so don't use it during periods of drought or very late autumn and winter. There is one caveat - glyphosate binds to soil particles and is present for some weeks, and there is some evidence that crops such as carrots did absorb glyphosate from treated ground post treatment. However, this is less likely with your bulbs - once the foliage has died back, the bulb is returning to dormancy, and by the time it starts growing again, any glyphosate in the soil should have disappeared. If, though, some of the bulbs are daffodils, their roots start growing in August, so I'd avoid treating that area much past the end of June, just in case they absorb the glyphosate. Other bulb roots start growing later in the year.