I live in Boulder, and I've done that exact trip on tour. So you could go (almost) the same way I did. I took two days because it's about 140 miles. You can camp overnight at any of numerous places in Poudre Canyon.
There are a lot of turns in the following directions, but many of the turns are easy to find because they occur at places where the road you are on ends. All of these except for getting out of Boulder on the diagonal (very wide shoulder) and 1 mile on US 34 (reasonable shoulder) are sleepy county roads (little to no shoulder).
Head northeast on the diagonal (highway 119) towards Longmont. Turn north on 63rd Street (recently repaved and very smooth now) for five miles until 63rd Street ends at Nelson. Take Nelson 1.5 miles east to 75th Street. Go north 5.5 miles on 75th Street through Hygiene (water available at the market) until it ends at Woodland. Take Woodland 2.5 miles east to where it ends at 95th Street (you cannot take 83rd north now because the bridge is out). Take 95th Street six miles north to where it ends at CR 10 (jogging one block west on Yellowstone after one mile). Take CR 10 one mile west to where it ends at CR 23. Take CR 23 two miles north to CR 12. Take CR 12 west. After 2 miles, it curves north and becomes CR 29. Take CR 29 five miles north to US Highway 34 (you can't take it any farther because the bridge is out). Take US 34 one mile east to CR 27. Take CR 27 five miles north to the tiny town of Masonville (small general store). Turn left at the stop sign onto Buckhorn Road/CR 27. Take this 20 rolling miles north to where it ends at Poudre Canyon Road/CR 14. Turn left (west). Now it's simple, but you have 65 miles of (mostly gentle) uphill. Continue on CR 14 for 72 miles to Walden, going over Cameron Pass (10,276').
There are several campgrounds in Poudre Canyon where you can get water or camp. You can also wild camp in Poudre Canyon, which is what I did. Take reasonable bear precautions.
When you get to Walden, you can shower at the town pool (for a small fee) and camp in the city park (for free). See if you can find the park manager so he will turn off the sprinklers. If you can't, you can sleep in the gazebo in the middle of the park.