Pretty much any time you find them available locally.......that's usually right around Labor Day. And you can plant as late as you are able before the ground freezes but I'd lean towards an earlier rather than a later planting so the roots have time to establish.

You do not have to dig up the bulbs, but can plant annuals around them. However, you do need to leave the tulips in place and the foliage intact until it dries and falls away naturally if you want a repeat show next spring. And they would prefer a dry situation during summer dormancy so may not be as compatible with annual plantings that require routine summer irrigation.

And finally, many modern tulips have a poor reputation for returning and blooming well in subsequent years. In fact, many gardeners treat them as annuals and replant each season. The Darwin hybrids and most species tulips are the best at perennializing.