In Sweden you can bring a bike as it is on many bus routes, most local trains and a few long distance trains - see the map below. On the rest of long distance trains you have to use a soft bicycle bag.
If you arrive by bike you may like to leave luggage at the start. You can use Roadfinder for finding good roads.
If you arrive by car there is parking space at Fyrishov sports centre near the finish. For multi-day parking you need a ticked bought in the reception. On Fyrishov there is also a camping site. Remember to rest properly before driving.
If you arrive by air you can take the SL commuter train from Arlanda C to Uppsala.
On this map is displayed train (various colors) and bus routes (grey) where in july 2018 you can bring a bicycle without case. If you pack you bike in a case you may bring it on a larger selection of trains, and Swebus Express coaches.
Local trains take bicycles on board: Tåg i Bergslagen, UL, SL, Öresundståg, Pågatåg, Krösatåg, Västtrafik, Östgötatrafiken Tranås-Norrköping, Värmlandstrafik, X-trafik and Norrtåg. In addition, TÅGAB (pink on map) allows bikes on board Göteborg-Karlstad-Stockholm and to Mora. On SJ, Snälltåget, Blå Tåget och MTR Expressen you have to remove wheels, turn your handlebars and put the bike in a case.
Between Västerås and Uppsala you have to use bus 874 with a change of buses in Enköping, not the direct bus 774 which do not allow bikes on board.
On most trains bike are transported if space is free in the bike racks. Prices vary between 0 kr (UL, SL, Västtrafik) and childrens' fee (Öresundstågen). Some stations, notably Stockholm C / Stockholm city or Arlanda C do not allow bikes without a case any time of the day.
If you wish to travel without a bicycle case you can for example use TÅGAB train 7010 from Göteborg 7:45, change in Kristinehamn to TÅBAG train 27056 arriving in Stockholm Södra 13:48. From there a SL commuter train leaves for Uppsala 14:07, arriving at 15:06. Book Göteborg-Stockholm Södra on sj.se, deselect high speed trains and select Kristinehamn as a middle halt.