Note: Am local to the area (Canadian side)
No, Uber/Lyft will not cross the border. They can take you there and drop you off, and get one on the other side.
QuickConnect or Flixbus will get you over the border into Vancouver. Be prepared that buses can and will be up to an hour delayed, as they often start their runs south of seattle, and any traffic issues will delay things. Also, the Bellingham Airport is not near anything else, so it is not walkable to the Amtrak station even if it were available (It is on the opposite side of Bellingham).
Do not try to rush the border. Ensure you have 2 hours budgeted for border delays (traffic + they have to clear your entire bus). If you get through faster, great!
On the plus side, Bellingham is a small airport, so luggage comes out fast. On the downside, Bellingham is a small airport, so you are walking on the tarmac to get on/off the plane, so it could rain on you.
Pay attention to where the bus drops off in Vancouver. Note that the cruise terminal and most hotels are around Waterfront, and that Grand Central Station (where many buses drop off) is NOT walkable to hotels (but is to the rapid transit), and is on the edge of a depressed area (so you will see some homeless people). It isn't unsafe, but be aware of what you may see.
Speaking of Uber/Lyft, make sure your phone plan can handle Canada. Don't be surprised by international charges.