Just hold down ALT while dragging the clip in the sequence. It'll create a copy, to which you can then apply the slow motion.
You may be over thinking this. There are easier ways. Jim's way is simple to use.
Or, how about this instead?
Put the clip on the timeline at full speed, then put it on the timeline again, and stretch the time to show it at 25% speed (for example). Put the title over the slower clip and that's it.
This example video shows me putting the video on the timeline, then putting in a title I have already prepared over a copy of the clip held on the last frame, then the same video but set for slow motion using Time Remapping.
If the clip had been longer, I would have eased into the slow motion gradually over the first three seconds or so, but this clip just wasn't long enough for that.
As Steven suggests, the Clip on the Timeline is but an Instance of the one in the Project Panel. You can have many Instances of a Clip, and each can be Trimmed differently, if necessary.