The best approach is to identify the firms you'd like to interview with and didn't get a slot for. Contact their recruiting people (the coordinator, not the hiring partner) and simply say hey I'm interested in your firm (you'd best know something about the firm), bid for it but didn't get it, can you fit me in? I've done this a few times, and every time the firm was super excited to hear from me and found a way for me to interview.
Also, this is where some prior networking helps - I went to many of those free 1L dinners and happy hours and met folks. Most everyone I talked to from those firms said that if I didn't do well in the bidding to be sure to contact them and they'd be sure to slot me in somewhere. To the extent I had reason to test this, they were all true to their word.
I would recommend against showing up to the hospitality suit unannounced as their schedules tend to be really packed, most firms end up getting a bit behind and chances of them being able to slot you in on the spot are not fantastic. Also it makes it look like you don't have your act together or really aren't all that interested in the firm. A bit of initiative ahead of time goes a long way. The earlier you can contact the firm the better, but even if its the day before they are interviewing you should have no problems.