So I tried to ferment in the bottling bucket and it's not working as planned

Ok so my girlfriend got me this wine making kit and we wanted to start the wine making process before she went away for a few weeks. I didn't have a bucket free so I decided, against my better judgement, to go ahead and ferment in the bottling bucket. The wine kit instructions said to rack to a secondary after only 5 days anyway so I figured 5 days would work. I woke up this morning and saw that there was some drippage from the spout. It's from the spout itself and it's not a leak that can be fixed through tightening it on the bucket. There isn't any activity in the airlock but I know that doesn't mean fermentation isn't happening or isn't gonna happen. I guess there's nothing I can do at this point to secure the bucket from leaking. I'll be getting the carboy to transfer into this weekend. My current plan is that I'll take a gravity reading after the 5 days and if it hasn't moved than I'll go ahead and transfer into the Carboy anyway and re-pitch some yeast to get the fermentation going. Does that sound like it would work? I really hope I didn't ruin my wine. I'll just try to RDWHAHB I guess.

It will probably be fine. I've fermented in bottling buckets before when I didn't have a normal bucket or carboy free. Once in awhile I've noticed dripping from the spout as well. Just cover it with a sanitized plastic sandwich bag if you're worried. I did that a couple of times, and the beer turned out fine.

If the gravity isn't dropping then at all for quite awhile then you could have just had some iffy yeast, and repitching will probably get things going.

Ive noticed if you turn the handle a little it doesnt drip as much assuming your talking about the airvent hole it drips from.

I have two buckets for brewing, they both have spigots, so they've both been used as primaries and bottling buckets. One of the spigots always leaks, and I can never remember which it is. The beer has always turned out fine, I trust yours will as well.

yea, I used to be lazy and ferment in bottling buckets as well without problems, though I didn't have leak problems. As for the leaks, just (lightly) hit yourself over the head and tighten it for next time if possible. Unless it's gushing, don't worry about it too much. Though the lack of airlock activity is probably your biggest concern. There's always a possibility that fermentation happened very quickly when you weren't looking (say overnight) since you may be dealing with highly fermentable sugar, or the lid isn't completely seated, it's a full moon, etc. You're right that you may want to take a gravity reading, and if it hasn't moved, you'd be right to want to pitch more yeast.