The situations are different.
In the bonus scene, Bumblestripe went to Dovewing because he wanted to see if they could go on a patrol later, but she accused him otherwise before realizing she was wrong and apologizing. To him, he wanted to get back together with Dovewing because he still feels the same about her, and that he realized life was short, he wanted to be with Dove and have kits together. However he only wanted her to think about it, he wasn't asking for an outright decision then. The only reason Dovewing is apparently not into the idea is not that she didn't want kits, but because she claims that now wasn't the time for it. (Which is ya know a lie considering she gets back with Tigerheart not long after and has his kits anyways.)
She also planned to work things out with Bumblestripe later, noting that she wanted to do that, but ironically, we all know that never happened. She never gave him a clear answer when she had plenty of chances to, and instead gave other excuses, and only really cared about being with her illegal mate. The said cat that no one knew about save for Ivypool and accidentally Twigpaw. So understandably it did come as a shock to Bumblestripe when she shows up later with another tom's kits from another clan, who also was the leader of ShadowClan, ya know the clan in hot controversy at the time.
Bumblestripe and Dovewing used to be mates, they're ex-mates now, the equivalent of ex-husband and wife, it's not odd for couples to rekindle relationships after breakups. It's literally happened before in the series, Squirrel and Bramble, and after getting together again they didn't take long to have kits after. Also, Crow and Night almost got back together, but Night was against. After they made up and worked things out, Crow wondered if they should have gotten back together again and Nightcloud wasn't into it.
The difference between Bumblestripe and Finleap is that Bumblestripe never emotionally tried to manipulate Dovewing into anything or guilt her. He made an offer to get back together because he wanted to try and work things out, he wasn't aware that there was another tom in the picture this whole time, and honestly, I don't blame him for that. It's not really his fault that Dovewing didn't know how to stay faithful to her own clan and was utterly fickle for two arcs. On the other hand, Finleap left his clan has an apprentice, for a girl. Sucked up to ThunderClan and got a bunch of praise, then constantly push the idea of kits. Like Dovewing, it wasn't that Twigbranch was against the idea of having kits, it's just that she wasn't ready for it. But whereas Dovewing's reasoning made no sense, it was honestly dumb, let's be real here, Twigbranch wanted to focus on her career as a first-time mentor. She actually made her stand clear, she told Finleap to his face, clearly said she wasn't ready, no, etc and didn't use some flimsy excuse, as Dovewing did.
When Finleap didn't like her standing her ground he ended up becoming a jerk, he tried to force her to choose between wanting to focus on her career or him and tried to guilt her into having kits. He got jealous of Tree, him of all cats lol, for talking to her. If anything, his behavior toward Twigbranch reminds me of how Dovewing manipulated Tigerheart and forced him to choose between her and his unborn kits and his dying clan that needed him for stability.
Also Bumblestripe's aggression toward Dovewing in the next book is well deserved. Why should he be obligated to be nice to her after she abandoned her clan just to be with a ShadowClan leader? She left without even a word, her clan spent days probably looking for her, and it turns out in the end she was getting cozy in ShadowClan after leading a wild goose chase. She left ThunderClan after betraying them, and also talks crap about them later, she shouldn't be coming back waltzing into their camp for personal visits. Your loyalty is to your clan. If she wants to see her family she left behind so badly she can wait until the gatherings. There's no reason for her to show back up in ThunderClan for personal visits after she made it clear on what she did, where she went and who's she's with now.