I'd agree electrolysis, whilst cheaper takes an age as the beautician is finding every hair, and isn't as effective as ILP.
I have had ILP at a salon on my chin/neck & top lip. It did reduce it, but as mine is hormonal it has come back (although not as bad). I think I would really need to keep going for top ups - which is what they suggest - but it is rather pricey to keep doing it.
You can only shave in-between rather than pluck, but doubt that would be an issue for your bikini line!
I paid up front to get a discount, there might be room to haggle eps if you go for more than one area.
I like the idea of the home kits, but I'd be worried about burning myself esp as my most visible hair is on my face - don't want to add burns to the excess hair - nice!!
I didn't find the treatment that painful. The worst bit was my top lip, think the hairs are the thickest there (nice). But it is over in a few mins and there is some satisfaction in thinking of the hair follicles dying!!
OP - you cannot do whilst pregnant, so you'd need to start the course (think I had 6 sessions over 4 months) knowing that isn't an issue, obviously not everybody on MN is contemplating pregnancy.
Good luck.