I think to answer this question, we need to distinguish between two different senses of experience. I quote from LDOCE:
- [U] knowledge or skill that you gain from doing a job or activity, or the process of doing this. It's about knowledge or skills
In this sense we can use of/in/with after experience to make noun phrases or gerund as in
You’ve got a lot of experience of lecturing.
my experience in many areas of the music business
in is often followed by a gerund. However noun phrases are also possible. 'Experience in' implies the person has been (professionally) trained in something (a special field of activity) as in
We need someone who has experience in marketing and teaching,
and after 'of', we mainly use gerund unless the word 'experience' is preceded by get/gain as in
The programme enables pupils to gain some experience of the world of work.
And afer with we tend to use noun phrases (persons/animals) and it implies that the knowledge has been gained about something by actual physical contact as in
I have experience with children.
Let's say this is said by a sister who raised his brother while his mom was always away working.
- [C] something that happens to you or something you do, especially when this has an effect on what you feel or think. It's about what happens.
In this sense we use of/with/for (Not in) after experience to make noun phrases as in
This was my first experience of living with other people.
In this sense, I think you can use both with and of interchangeably to make the same meaning as in
It was her first experience of/with dealing with people from another culture.
I assume you try to refer to loving someone simply as an event, or type of event, lived through which does not have the idea of gained knowledge. So, I think sentence two is the safest choice here. About number one (experience doing something) I found no reference to back it up so I think it's better to be avoided at least when formality matters. Many think of it as acceptable though as in
She has a great deal of experience (in) introducing new products to international markets.