As you're probably aware there are many things that can derail IPO -- bad market timing, etc, though this seems to be getting better with Snap announcing their IPO. If that IPO bombs, it might have a negative impact for a few weeks but the roll back in bank regulations could also help. If a competitor is on track to IPO, couldn't your existing company be considering this route too? Maybe you can negotiate more options with existing company, at a lower valuation, and see if they are going to do a dividend payout in near future and this could generate additional wealth on the way to IPO. If your existing company decides to IPO, they may already be planning it and timing to right after the competitor in order to gain momentum for their stock price or hold off if it is negative.
As for burning bridges, this part is tricky because everyone knows people job hop around looking for bigger payout. When new company IPO happens, there will likely be a holding period before you can start selling stock so you need to know timeframes from them too.