I think your best bet would probably be to pathwalk to Asgard via a physical space that resonates with it. Otherwise, you could just project straight to it if you're proficient in projection or get the aid of one of the Aesir or Asynjur.
Also note that the Aesir/Asynjur are not the only Gods in Norse Paganism. There's also the Vanir and (some would consider) the Jotnar. Personally, I view all of the Vaettir as having the capability of being a God as the ones I work with are ones I have deep reverence and respect for (I personally include the Dokkalfar in Rokkatru and the Dvergar can be held as Gods of craftmanship in their own right).
If you're wanting to travel to Asgard via Bifrost, then I would not recommend calling upon the aid of Thor as he is cited in the lore as being too heavy to cross it (so he has to wade through the river below it). Honestly, Sleipnir and Odin would be good bets on aiding your travels there.
To add on to what you were saying if i might, A good example of a Giantess being accepted as a Goddess is Skadi. Also Traveling to such places can be as dangrous as it can be awe inspiring. A lot of ways to offend Deities or beings you might come across in that respect. There are a lot of different this and thats to go over, but if your new i honestly wouldnt attempt this right off the bat. If you have experience in pathwalking or astral traveling then that is fine but there are always risks. Another God that can aid in traveling the Nine worlds is Freyr, but of course then that requires some experience in working with deities on at least a basic lvl. Baby steps is a good analogy.
Much like Odins steed, Freyr's boar is said to carry him and great speed throughout the nine worlds. Thats in the versions ive read at least. It seems like he would be good to call upon when traveling to such realms. But most people do typically think of Odin when they think of an aid in such travels, i suppose its all on preferance but thats just my opinion.
Journeying & Pathwalking by Personified
I can't find direct reference of it at the moment, though I did see an article on folk using runes and bindrunes to aid in Pathwalking, visually and in the form of Galdrar. This is another possibility to look into if you're interested. Heathenry traditionally doesn't have very many magical practices and "spells" have a very specific concept in Norse Pagan history that isn't quite what people commonly treat as spell-work in modern communities. Does this mean you can't use a spell to aid you? Not at all; just realize it's not a historical thing.